सोडोवचें f(x)=(x^2+4x+3/x^2+2x-3-x^2+2x+1/x^2+3x+2)*x+2/x+1

$$f ( x ) = ( \frac { x ^ { 2 } + 4 x + 3 } { x ^ { 2 } + 2 x - 3 } - \frac { x ^ { 2 } + 2 x + 1 } { x ^ { 2 } + 3 x + 2 } ) \cdot \frac { x + 2 } { x + 1 }$$

मूल्यांकन करचें

$$\frac{3}{x-1}$$

संक्षिप्त समाधान पांवडे

\frac{x^{2}+4x+3}{x^{2}+2x-3} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\left(\frac{\left(x+1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}-\frac{x^{2}+2x+1}{x^{2}+3x+2}\right)\times \frac{x+2}{x+1}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x+3 रद्द करचो.

$$\left(\frac{x+1}{x-1}-\frac{x^{2}+2x+1}{x^{2}+3x+2}\right)\times \frac{x+2}{x+1}$$

\frac{x^{2}+2x+1}{x^{2}+3x+2} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\left(\frac{x+1}{x-1}-\frac{\left(x+1\right)^{2}}{\left(x+1\right)\left(x+2\right)}\right)\times \frac{x+2}{x+1}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x+1 रद्द करचो.

$$\left(\frac{x+1}{x-1}-\frac{x+1}{x+2}\right)\times \frac{x+2}{x+1}$$

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

$$\left(\frac{\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)}-\frac{\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)}\right)\times \frac{x+2}{x+1}$$

\frac{\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)} आनी \frac{\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर वजा करून तांची वजाबाकी करची.

$$\frac{\left(x+1\right)\left(x+2\right)-\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)}\times \frac{x+2}{x+1}$$

\left(x+1\right)\left(x+2\right)-\left(x+1\right)\left(x-1\right) त गुणाकार करचे.

$$\frac{x^{2}+2x+x+2-x^{2}+x-x+1}{\left(x-1\right)\left(x+2\right)}\times \frac{x+2}{x+1}$$

x^{2}+2x+x+2-x^{2}+x-x+1 त समान शब्द एकठांय करचे.

$$\frac{3x+3}{\left(x-1\right)\left(x+2\right)}\times \frac{x+2}{x+1}$$

न्युमरेटर वेळा न्युमरेटराक आनी डिनोमिनेटर वेळा डिनोमिनेटराक गुणून \frac{x+2}{x+1} वेळा \frac{3x+3}{\left(x-1\right)\left(x+2\right)} गुणचें.

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

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x+2 रद्द करचो.

$$\frac{3x+3}{\left(x-1\right)\left(x+1\right)}$$

आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\frac{3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x+1 रद्द करचो.

$$\frac{3}{x-1}$$

विस्तार करचो

$$\frac{3}{x-1}$$

संक्षिप्त समाधान पांवडे

\frac{x^{2}+4x+3}{x^{2}+2x-3} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\left(\frac{\left(x+1\right)\left(x+3\right)}{\left(x-1\right)\left(x+3\right)}-\frac{x^{2}+2x+1}{x^{2}+3x+2}\right)\times \frac{x+2}{x+1}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x+3 रद्द करचो.

$$\left(\frac{x+1}{x-1}-\frac{x^{2}+2x+1}{x^{2}+3x+2}\right)\times \frac{x+2}{x+1}$$

\frac{x^{2}+2x+1}{x^{2}+3x+2} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\left(\frac{x+1}{x-1}-\frac{\left(x+1\right)^{2}}{\left(x+1\right)\left(x+2\right)}\right)\times \frac{x+2}{x+1}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x+1 रद्द करचो.

$$\left(\frac{x+1}{x-1}-\frac{x+1}{x+2}\right)\times \frac{x+2}{x+1}$$

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

$$\left(\frac{\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)}-\frac{\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)}\right)\times \frac{x+2}{x+1}$$

\frac{\left(x+1\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)} आनी \frac{\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर वजा करून तांची वजाबाकी करची.

$$\frac{\left(x+1\right)\left(x+2\right)-\left(x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x+2\right)}\times \frac{x+2}{x+1}$$

\left(x+1\right)\left(x+2\right)-\left(x+1\right)\left(x-1\right) त गुणाकार करचे.

$$\frac{x^{2}+2x+x+2-x^{2}+x-x+1}{\left(x-1\right)\left(x+2\right)}\times \frac{x+2}{x+1}$$

x^{2}+2x+x+2-x^{2}+x-x+1 त समान शब्द एकठांय करचे.

$$\frac{3x+3}{\left(x-1\right)\left(x+2\right)}\times \frac{x+2}{x+1}$$

न्युमरेटर वेळा न्युमरेटराक आनी डिनोमिनेटर वेळा डिनोमिनेटराक गुणून \frac{x+2}{x+1} वेळा \frac{3x+3}{\left(x-1\right)\left(x+2\right)} गुणचें.

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

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x+2 रद्द करचो.

$$\frac{3x+3}{\left(x-1\right)\left(x+1\right)}$$

आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\frac{3\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x+1 रद्द करचो.

$$\frac{3}{x-1}$$