सोडोवचें 1/4+1/4n+2+1/2left(2n+4right)-1/2n+1

$$\frac{ 1 }{ 4 } + \frac{ 1 }{ 4n+2 } + \frac{ 1 }{ 2 \left( 2n+4 \right) } - \frac{ 1 }{ 2n+1 }$$

मूल्यांकन करचें

$$\frac{2n^{2}+5n-1}{4\left(n+2\right)\left(2n+1\right)}$$

संक्षिप्त समाधान पांवडे

4n+2 गुणकपद काडचें.

$$\frac{1}{4}+\frac{1}{2\left(2n+1\right)}+\frac{1}{2\left(2n+4\right)}-\frac{1}{2n+1}$$

ऍक्सप्रेशन जमा करूंक वा वजा करूंक, तांचे डिनोमिनेटर तसोच दवरूंक विस्तारावचें. 4 आनी 2\left(2n+1\right) चो किमान सामान्य गुणाकार आसा 4\left(2n+1\right). \frac{2n+1}{2n+1}क \frac{1}{4} फावटी गुणचें. \frac{2}{2}क \frac{1}{2\left(2n+1\right)} फावटी गुणचें.

$$\frac{2n+1}{4\left(2n+1\right)}+\frac{2}{4\left(2n+1\right)}+\frac{1}{2\left(2n+4\right)}-\frac{1}{2n+1}$$

\frac{2n+1}{4\left(2n+1\right)} आनी \frac{2}{4\left(2n+1\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर जो़डून तांची बेरीज करची.

$$\frac{2n+1+2}{4\left(2n+1\right)}+\frac{1}{2\left(2n+4\right)}-\frac{1}{2n+1}$$

2n+1+2 त समान शब्द एकठांय करचे.

$$\frac{2n+3}{4\left(2n+1\right)}+\frac{1}{2\left(2n+4\right)}-\frac{1}{2n+1}$$

2\left(2n+4\right) गुणकपद काडचें.

$$\frac{2n+3}{4\left(2n+1\right)}+\frac{1}{2^{2}\left(n+2\right)}-\frac{1}{2n+1}$$

ऍक्सप्रेशन जमा करूंक वा वजा करूंक, तांचे डिनोमिनेटर तसोच दवरूंक विस्तारावचें. 4\left(2n+1\right) आनी 2^{2}\left(n+2\right) चो किमान सामान्य गुणाकार आसा 4\left(n+2\right)\left(2n+1\right). \frac{n+2}{n+2}क \frac{2n+3}{4\left(2n+1\right)} फावटी गुणचें. \frac{2n+1}{2n+1}क \frac{1}{2^{2}\left(n+2\right)} फावटी गुणचें.

$$\frac{\left(2n+3\right)\left(n+2\right)}{4\left(n+2\right)\left(2n+1\right)}+\frac{2n+1}{4\left(n+2\right)\left(2n+1\right)}-\frac{1}{2n+1}$$

\frac{\left(2n+3\right)\left(n+2\right)}{4\left(n+2\right)\left(2n+1\right)} आनी \frac{2n+1}{4\left(n+2\right)\left(2n+1\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर जो़डून तांची बेरीज करची.

$$\frac{\left(2n+3\right)\left(n+2\right)+2n+1}{4\left(n+2\right)\left(2n+1\right)}-\frac{1}{2n+1}$$

\left(2n+3\right)\left(n+2\right)+2n+1 त गुणाकार करचे.

$$\frac{2n^{2}+4n+3n+6+2n+1}{4\left(n+2\right)\left(2n+1\right)}-\frac{1}{2n+1}$$

2n^{2}+4n+3n+6+2n+1 त समान शब्द एकठांय करचे.

$$\frac{2n^{2}+9n+7}{4\left(n+2\right)\left(2n+1\right)}-\frac{1}{2n+1}$$

ऍक्सप्रेशन जमा करूंक वा वजा करूंक, तांचे डिनोमिनेटर तसोच दवरूंक विस्तारावचें. 4\left(n+2\right)\left(2n+1\right) आनी 2n+1 चो किमान सामान्य गुणाकार आसा 4\left(n+2\right)\left(2n+1\right). \frac{4\left(n+2\right)}{4\left(n+2\right)}क \frac{1}{2n+1} फावटी गुणचें.

$$\frac{2n^{2}+9n+7}{4\left(n+2\right)\left(2n+1\right)}-\frac{4\left(n+2\right)}{4\left(n+2\right)\left(2n+1\right)}$$

\frac{2n^{2}+9n+7}{4\left(n+2\right)\left(2n+1\right)} आनी \frac{4\left(n+2\right)}{4\left(n+2\right)\left(2n+1\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर वजा करून तांची वजाबाकी करची.

$$\frac{2n^{2}+9n+7-4\left(n+2\right)}{4\left(n+2\right)\left(2n+1\right)}$$

2n^{2}+9n+7-4\left(n+2\right) त गुणाकार करचे.

$$\frac{2n^{2}+9n+7-4n-8}{4\left(n+2\right)\left(2n+1\right)}$$

2n^{2}+9n+7-4n-8 त समान शब्द एकठांय करचे.

$$\frac{2n^{2}+5n-1}{4\left(n+2\right)\left(2n+1\right)}$$

\frac{2n^{2}+5n-1}{4\left(n+2\right)\left(2n+1\right)} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\frac{2\left(n-\left(-\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{4\left(n+2\right)\left(2n+1\right)}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय 2 रद्द करचो.

$$\frac{\left(n-\left(-\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{2\left(n+2\right)\left(2n+1\right)}$$

2\left(n+2\right)\left(2n+1\right) विस्तारीत करचो.

$$\frac{\left(n-\left(-\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{4n^{2}+10n+4}$$

-\frac{1}{4}\sqrt{33}-\frac{5}{4} चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\frac{\left(n-\left(-\frac{1}{4}\sqrt{33}\right)-\left(-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{4n^{2}+10n+4}$$

-\frac{1}{4}\sqrt{33} च्या विरुध्दार्थी अंक \frac{1}{4}\sqrt{33} आसा.

$$\frac{\left(n+\frac{1}{4}\sqrt{33}-\left(-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{4n^{2}+10n+4}$$

-\frac{5}{4} च्या विरुध्दार्थी अंक \frac{5}{4} आसा.

$$\frac{\left(n+\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{4n^{2}+10n+4}$$

\frac{1}{4}\sqrt{33}-\frac{5}{4} चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\frac{\left(n+\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\left(n-\frac{1}{4}\sqrt{33}-\left(-\frac{5}{4}\right)\right)}{4n^{2}+10n+4}$$

-\frac{5}{4} च्या विरुध्दार्थी अंक \frac{5}{4} आसा.

$$\frac{\left(n+\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\left(n-\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)}{4n^{2}+10n+4}$$

n+\frac{1}{4}\sqrt{33}+\frac{5}{4}च्या प्रत्येकी टर्माक n-\frac{1}{4}\sqrt{33}+\frac{5}{4} च्या प्रत्येकी टर्मान गुणाकार करून वितरक गुणधर्म लागू करचो.

$$\frac{n^{2}+n\left(-\frac{1}{4}\right)\sqrt{33}+n\times \frac{5}{4}+\frac{1}{4}\sqrt{33}n+\frac{1}{4}\sqrt{33}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

33 मेळोवंक \sqrt{33} आनी \sqrt{33} गुणचें.

$$\frac{n^{2}+n\left(-\frac{1}{4}\right)\sqrt{33}+n\times \frac{5}{4}+\frac{1}{4}\sqrt{33}n+\frac{1}{4}\times 33\left(-\frac{1}{4}\right)+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

0 मेळोवंक n\left(-\frac{1}{4}\right)\sqrt{33} आनी \frac{1}{4}\sqrt{33}n एकठांय करचें.

$$\frac{n^{2}+n\times \frac{5}{4}+\frac{1}{4}\times 33\left(-\frac{1}{4}\right)+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

\frac{33}{4} मेळोवंक \frac{1}{4} आनी 33 गुणचें.

$$\frac{n^{2}+n\times \frac{5}{4}+\frac{33}{4}\left(-\frac{1}{4}\right)+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

न्युमरेटर वेळा न्युमरेटराक आनी डिनोमिनेटर वेळा डिनोमिनेटराक गुणून -\frac{1}{4} वेळा \frac{33}{4} गुणचें.

$$\frac{n^{2}+n\times \frac{5}{4}+\frac{33\left(-1\right)}{4\times 4}+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

फ्रॅक्शन \frac{33\left(-1\right)}{4\times 4} त गुणाकार करचे.

$$\frac{n^{2}+n\times \frac{5}{4}+\frac{-33}{16}+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

नकारात्मक चिन्न वगळावंन अपुर्णांक \frac{-33}{16} हो -\frac{33}{16} भशेन परत बरोवंक शकतात.

$$\frac{n^{2}+n\times \frac{5}{4}-\frac{33}{16}+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

न्युमरेटर वेळा न्युमरेटराक आनी डिनोमिनेटर वेळा डिनोमिनेटराक गुणून \frac{5}{4} वेळा \frac{1}{4} गुणचें.

$$\frac{n^{2}+n\times \frac{5}{4}-\frac{33}{16}+\frac{1\times 5}{4\times 4}\sqrt{33}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

फ्रॅक्शन \frac{1\times 5}{4\times 4} त गुणाकार करचे.

$$\frac{n^{2}+n\times \frac{5}{4}-\frac{33}{16}+\frac{5}{16}\sqrt{33}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

\frac{5}{2}n मेळोवंक n\times \frac{5}{4} आनी \frac{5}{4}n एकठांय करचें.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5}{16}\sqrt{33}+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

न्युमरेटर वेळा न्युमरेटराक आनी डिनोमिनेटर वेळा डिनोमिनेटराक गुणून -\frac{1}{4} वेळा \frac{5}{4} गुणचें.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5}{16}\sqrt{33}+\frac{5\left(-1\right)}{4\times 4}\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

फ्रॅक्शन \frac{5\left(-1\right)}{4\times 4} त गुणाकार करचे.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5}{16}\sqrt{33}+\frac{-5}{16}\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

नकारात्मक चिन्न वगळावंन अपुर्णांक \frac{-5}{16} हो -\frac{5}{16} भशेन परत बरोवंक शकतात.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5}{16}\sqrt{33}-\frac{5}{16}\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

0 मेळोवंक \frac{5}{16}\sqrt{33} आनी -\frac{5}{16}\sqrt{33} एकठांय करचें.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

न्युमरेटर वेळा न्युमरेटराक आनी डिनोमिनेटर वेळा डिनोमिनेटराक गुणून \frac{5}{4} वेळा \frac{5}{4} गुणचें.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5\times 5}{4\times 4}}{4n^{2}+10n+4}$$

फ्रॅक्शन \frac{5\times 5}{4\times 4} त गुणाकार करचे.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{25}{16}}{4n^{2}+10n+4}$$

-\frac{33}{16} आनी \frac{25}{16} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर जो़डून तांची बेरीज करची.

$$\frac{n^{2}+\frac{5}{2}n+\frac{-33+25}{16}}{4n^{2}+10n+4}$$

-8 मेळोवंक -33 आनी 25 ची बेरीज करची.

$$\frac{n^{2}+\frac{5}{2}n+\frac{-8}{16}}{4n^{2}+10n+4}$$

8 भायर काडून आनी रद्द करून एकदम उण्या संज्ञेत अपुर्णांक \frac{-8}{16} उणो करचो.

$$\frac{n^{2}+\frac{5}{2}n-\frac{1}{2}}{4n^{2}+10n+4}$$

आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\frac{\frac{1}{2}\times 2\left(n-\left(-\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{2\left(n+2\right)\left(2n+1\right)}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय 2 रद्द करचो.

$$\frac{\frac{1}{2}\left(n-\left(-\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{\left(n+2\right)\left(2n+1\right)}$$

ऍक्सप्रेशन विस्तारचें.

$$\frac{\frac{1}{2}n^{2}+\frac{5}{4}n-\frac{1}{4}}{2n^{2}+5n+2}$$

विस्तार करचो

$$\frac{2n^{2}+5n-1}{4\left(n+2\right)\left(2n+1\right)}$$

संक्षिप्त समाधान पांवडे

4n+2 गुणकपद काडचें.

$$\frac{1}{4}+\frac{1}{2\left(2n+1\right)}+\frac{1}{2\left(2n+4\right)}-\frac{1}{2n+1}$$

ऍक्सप्रेशन जमा करूंक वा वजा करूंक, तांचे डिनोमिनेटर तसोच दवरूंक विस्तारावचें. 4 आनी 2\left(2n+1\right) चो किमान सामान्य गुणाकार आसा 4\left(2n+1\right). \frac{2n+1}{2n+1}क \frac{1}{4} फावटी गुणचें. \frac{2}{2}क \frac{1}{2\left(2n+1\right)} फावटी गुणचें.

$$\frac{2n+1}{4\left(2n+1\right)}+\frac{2}{4\left(2n+1\right)}+\frac{1}{2\left(2n+4\right)}-\frac{1}{2n+1}$$

\frac{2n+1}{4\left(2n+1\right)} आनी \frac{2}{4\left(2n+1\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर जो़डून तांची बेरीज करची.

$$\frac{2n+1+2}{4\left(2n+1\right)}+\frac{1}{2\left(2n+4\right)}-\frac{1}{2n+1}$$

2n+1+2 त समान शब्द एकठांय करचे.

$$\frac{2n+3}{4\left(2n+1\right)}+\frac{1}{2\left(2n+4\right)}-\frac{1}{2n+1}$$

2\left(2n+4\right) गुणकपद काडचें.

$$\frac{2n+3}{4\left(2n+1\right)}+\frac{1}{2^{2}\left(n+2\right)}-\frac{1}{2n+1}$$

ऍक्सप्रेशन जमा करूंक वा वजा करूंक, तांचे डिनोमिनेटर तसोच दवरूंक विस्तारावचें. 4\left(2n+1\right) आनी 2^{2}\left(n+2\right) चो किमान सामान्य गुणाकार आसा 4\left(n+2\right)\left(2n+1\right). \frac{n+2}{n+2}क \frac{2n+3}{4\left(2n+1\right)} फावटी गुणचें. \frac{2n+1}{2n+1}क \frac{1}{2^{2}\left(n+2\right)} फावटी गुणचें.

$$\frac{\left(2n+3\right)\left(n+2\right)}{4\left(n+2\right)\left(2n+1\right)}+\frac{2n+1}{4\left(n+2\right)\left(2n+1\right)}-\frac{1}{2n+1}$$

\frac{\left(2n+3\right)\left(n+2\right)}{4\left(n+2\right)\left(2n+1\right)} आनी \frac{2n+1}{4\left(n+2\right)\left(2n+1\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर जो़डून तांची बेरीज करची.

$$\frac{\left(2n+3\right)\left(n+2\right)+2n+1}{4\left(n+2\right)\left(2n+1\right)}-\frac{1}{2n+1}$$

\left(2n+3\right)\left(n+2\right)+2n+1 त गुणाकार करचे.

$$\frac{2n^{2}+4n+3n+6+2n+1}{4\left(n+2\right)\left(2n+1\right)}-\frac{1}{2n+1}$$

2n^{2}+4n+3n+6+2n+1 त समान शब्द एकठांय करचे.

$$\frac{2n^{2}+9n+7}{4\left(n+2\right)\left(2n+1\right)}-\frac{1}{2n+1}$$

ऍक्सप्रेशन जमा करूंक वा वजा करूंक, तांचे डिनोमिनेटर तसोच दवरूंक विस्तारावचें. 4\left(n+2\right)\left(2n+1\right) आनी 2n+1 चो किमान सामान्य गुणाकार आसा 4\left(n+2\right)\left(2n+1\right). \frac{4\left(n+2\right)}{4\left(n+2\right)}क \frac{1}{2n+1} फावटी गुणचें.

$$\frac{2n^{2}+9n+7}{4\left(n+2\right)\left(2n+1\right)}-\frac{4\left(n+2\right)}{4\left(n+2\right)\left(2n+1\right)}$$

\frac{2n^{2}+9n+7}{4\left(n+2\right)\left(2n+1\right)} आनी \frac{4\left(n+2\right)}{4\left(n+2\right)\left(2n+1\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर वजा करून तांची वजाबाकी करची.

$$\frac{2n^{2}+9n+7-4\left(n+2\right)}{4\left(n+2\right)\left(2n+1\right)}$$

2n^{2}+9n+7-4\left(n+2\right) त गुणाकार करचे.

$$\frac{2n^{2}+9n+7-4n-8}{4\left(n+2\right)\left(2n+1\right)}$$

2n^{2}+9n+7-4n-8 त समान शब्द एकठांय करचे.

$$\frac{2n^{2}+5n-1}{4\left(n+2\right)\left(2n+1\right)}$$

\frac{2n^{2}+5n-1}{4\left(n+2\right)\left(2n+1\right)} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\frac{2\left(n-\left(-\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{4\left(n+2\right)\left(2n+1\right)}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय 2 रद्द करचो.

$$\frac{\left(n-\left(-\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{2\left(n+2\right)\left(2n+1\right)}$$

2\left(n+2\right)\left(2n+1\right) विस्तारीत करचो.

$$\frac{\left(n-\left(-\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{4n^{2}+10n+4}$$

-\frac{1}{4}\sqrt{33}-\frac{5}{4} चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\frac{\left(n-\left(-\frac{1}{4}\sqrt{33}\right)-\left(-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{4n^{2}+10n+4}$$

-\frac{1}{4}\sqrt{33} च्या विरुध्दार्थी अंक \frac{1}{4}\sqrt{33} आसा.

$$\frac{\left(n+\frac{1}{4}\sqrt{33}-\left(-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{4n^{2}+10n+4}$$

-\frac{5}{4} च्या विरुध्दार्थी अंक \frac{5}{4} आसा.

$$\frac{\left(n+\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{4n^{2}+10n+4}$$

\frac{1}{4}\sqrt{33}-\frac{5}{4} चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

$$\frac{\left(n+\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\left(n-\frac{1}{4}\sqrt{33}-\left(-\frac{5}{4}\right)\right)}{4n^{2}+10n+4}$$

-\frac{5}{4} च्या विरुध्दार्थी अंक \frac{5}{4} आसा.

$$\frac{\left(n+\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)\left(n-\frac{1}{4}\sqrt{33}+\frac{5}{4}\right)}{4n^{2}+10n+4}$$

n+\frac{1}{4}\sqrt{33}+\frac{5}{4}च्या प्रत्येकी टर्माक n-\frac{1}{4}\sqrt{33}+\frac{5}{4} च्या प्रत्येकी टर्मान गुणाकार करून वितरक गुणधर्म लागू करचो.

$$\frac{n^{2}+n\left(-\frac{1}{4}\right)\sqrt{33}+n\times \frac{5}{4}+\frac{1}{4}\sqrt{33}n+\frac{1}{4}\sqrt{33}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

33 मेळोवंक \sqrt{33} आनी \sqrt{33} गुणचें.

$$\frac{n^{2}+n\left(-\frac{1}{4}\right)\sqrt{33}+n\times \frac{5}{4}+\frac{1}{4}\sqrt{33}n+\frac{1}{4}\times 33\left(-\frac{1}{4}\right)+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

0 मेळोवंक n\left(-\frac{1}{4}\right)\sqrt{33} आनी \frac{1}{4}\sqrt{33}n एकठांय करचें.

$$\frac{n^{2}+n\times \frac{5}{4}+\frac{1}{4}\times 33\left(-\frac{1}{4}\right)+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

\frac{33}{4} मेळोवंक \frac{1}{4} आनी 33 गुणचें.

$$\frac{n^{2}+n\times \frac{5}{4}+\frac{33}{4}\left(-\frac{1}{4}\right)+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

न्युमरेटर वेळा न्युमरेटराक आनी डिनोमिनेटर वेळा डिनोमिनेटराक गुणून -\frac{1}{4} वेळा \frac{33}{4} गुणचें.

$$\frac{n^{2}+n\times \frac{5}{4}+\frac{33\left(-1\right)}{4\times 4}+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

फ्रॅक्शन \frac{33\left(-1\right)}{4\times 4} त गुणाकार करचे.

$$\frac{n^{2}+n\times \frac{5}{4}+\frac{-33}{16}+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

नकारात्मक चिन्न वगळावंन अपुर्णांक \frac{-33}{16} हो -\frac{33}{16} भशेन परत बरोवंक शकतात.

$$\frac{n^{2}+n\times \frac{5}{4}-\frac{33}{16}+\frac{1}{4}\sqrt{33}\times \frac{5}{4}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

न्युमरेटर वेळा न्युमरेटराक आनी डिनोमिनेटर वेळा डिनोमिनेटराक गुणून \frac{5}{4} वेळा \frac{1}{4} गुणचें.

$$\frac{n^{2}+n\times \frac{5}{4}-\frac{33}{16}+\frac{1\times 5}{4\times 4}\sqrt{33}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

फ्रॅक्शन \frac{1\times 5}{4\times 4} त गुणाकार करचे.

$$\frac{n^{2}+n\times \frac{5}{4}-\frac{33}{16}+\frac{5}{16}\sqrt{33}+\frac{5}{4}n+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

\frac{5}{2}n मेळोवंक n\times \frac{5}{4} आनी \frac{5}{4}n एकठांय करचें.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5}{16}\sqrt{33}+\frac{5}{4}\left(-\frac{1}{4}\right)\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

न्युमरेटर वेळा न्युमरेटराक आनी डिनोमिनेटर वेळा डिनोमिनेटराक गुणून -\frac{1}{4} वेळा \frac{5}{4} गुणचें.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5}{16}\sqrt{33}+\frac{5\left(-1\right)}{4\times 4}\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

फ्रॅक्शन \frac{5\left(-1\right)}{4\times 4} त गुणाकार करचे.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5}{16}\sqrt{33}+\frac{-5}{16}\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

नकारात्मक चिन्न वगळावंन अपुर्णांक \frac{-5}{16} हो -\frac{5}{16} भशेन परत बरोवंक शकतात.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5}{16}\sqrt{33}-\frac{5}{16}\sqrt{33}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

0 मेळोवंक \frac{5}{16}\sqrt{33} आनी -\frac{5}{16}\sqrt{33} एकठांय करचें.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5}{4}\times \frac{5}{4}}{4n^{2}+10n+4}$$

न्युमरेटर वेळा न्युमरेटराक आनी डिनोमिनेटर वेळा डिनोमिनेटराक गुणून \frac{5}{4} वेळा \frac{5}{4} गुणचें.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{5\times 5}{4\times 4}}{4n^{2}+10n+4}$$

फ्रॅक्शन \frac{5\times 5}{4\times 4} त गुणाकार करचे.

$$\frac{n^{2}+\frac{5}{2}n-\frac{33}{16}+\frac{25}{16}}{4n^{2}+10n+4}$$

-\frac{33}{16} आनी \frac{25}{16} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर जो़डून तांची बेरीज करची.

$$\frac{n^{2}+\frac{5}{2}n+\frac{-33+25}{16}}{4n^{2}+10n+4}$$

-8 मेळोवंक -33 आनी 25 ची बेरीज करची.

$$\frac{n^{2}+\frac{5}{2}n+\frac{-8}{16}}{4n^{2}+10n+4}$$

8 भायर काडून आनी रद्द करून एकदम उण्या संज्ञेत अपुर्णांक \frac{-8}{16} उणो करचो.

$$\frac{n^{2}+\frac{5}{2}n-\frac{1}{2}}{4n^{2}+10n+4}$$

आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\frac{\frac{1}{2}\times 2\left(n-\left(-\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{2\left(n+2\right)\left(2n+1\right)}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय 2 रद्द करचो.

$$\frac{\frac{1}{2}\left(n-\left(-\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)\left(n-\left(\frac{1}{4}\sqrt{33}-\frac{5}{4}\right)\right)}{\left(n+2\right)\left(2n+1\right)}$$

ऍक्सप्रेशन विस्तारचें.

$$\frac{\frac{1}{2}n^{2}+\frac{5}{4}n-\frac{1}{4}}{2n^{2}+5n+2}$$