सोडोवचें x/x^2+10x+24-4/x^2+6x+8

$$\frac { x } { x ^ { 2 } + 10 x + 24 } - \frac { 4 } { x ^ { 2 } + 6 x + 8 }$$

मूल्यांकन करचें

$$\frac{x-6}{\left(x+2\right)\left(x+6\right)}$$

संक्षिप्त समाधान पांवडे

x^{2}+10x+24 गुणकपद काडचें. x^{2}+6x+8 गुणकपद काडचें.

$$\frac{x}{\left(x+4\right)\left(x+6\right)}-\frac{4}{\left(x+2\right)\left(x+4\right)}$$

ऍक्सप्रेशन जमा करूंक वा वजा करूंक, तांचे डिनोमिनेटर तसोच दवरूंक विस्तारावचें. \left(x+4\right)\left(x+6\right) आनी \left(x+2\right)\left(x+4\right) चो किमान सामान्य गुणाकार आसा \left(x+2\right)\left(x+4\right)\left(x+6\right). \frac{x+2}{x+2}क \frac{x}{\left(x+4\right)\left(x+6\right)} फावटी गुणचें. \frac{x+6}{x+6}क \frac{4}{\left(x+2\right)\left(x+4\right)} फावटी गुणचें.

$$\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}-\frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} आनी \frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर वजा करून तांची वजाबाकी करची.

$$\frac{x\left(x+2\right)-4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

x\left(x+2\right)-4\left(x+6\right) त गुणाकार करचे.

$$\frac{x^{2}+2x-4x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

x^{2}+2x-4x-24 त समान शब्द एकठांय करचे.

$$\frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

\frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\frac{\left(x-6\right)\left(x+4\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x+4 रद्द करचो.

$$\frac{x-6}{\left(x+2\right)\left(x+6\right)}$$

\left(x+2\right)\left(x+6\right) विस्तारीत करचो.

$$\frac{x-6}{x^{2}+8x+12}$$

w.r.t. x चो फरक काडचो

$$\frac{60+12x-x^{2}}{x^{4}+16x^{3}+88x^{2}+192x+144}$$

गुणकारा खातीर व्यत्पन्न नेम वापरून पांवडे

x^{2}+10x+24 गुणकपद काडचें. x^{2}+6x+8 गुणकपद काडचें.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(x+4\right)\left(x+6\right)}-\frac{4}{\left(x+2\right)\left(x+4\right)})$$

ऍक्सप्रेशन जमा करूंक वा वजा करूंक, तांचे डिनोमिनेटर तसोच दवरूंक विस्तारावचें. \left(x+4\right)\left(x+6\right) आनी \left(x+2\right)\left(x+4\right) चो किमान सामान्य गुणाकार आसा \left(x+2\right)\left(x+4\right)\left(x+6\right). \frac{x+2}{x+2}क \frac{x}{\left(x+4\right)\left(x+6\right)} फावटी गुणचें. \frac{x+6}{x+6}क \frac{4}{\left(x+2\right)\left(x+4\right)} फावटी गुणचें.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}-\frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} आनी \frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर वजा करून तांची वजाबाकी करची.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(x+2\right)-4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

x\left(x+2\right)-4\left(x+6\right) त गुणाकार करचे.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+2x-4x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

x^{2}+2x-4x-24 त समान शब्द एकठांय करचे.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

\frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} आदींच फॅक्टर्ड नाशिल्लें ऍक्सप्रेशन फॅक्ट करचें.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-6\right)\left(x+4\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

न्युमरेटर आनी डिनोमिनेटर अशा दोगांचेरूय x+4 रद्द करचो.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x-6}{\left(x+2\right)\left(x+6\right)})$$

वितरक गूणधर्माचो वापर करून x+2 क x+6 न गुणचें आनी संज्ञां भशेन एकठावणी करची.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x-6}{x^{2}+8x+12})$$

खंयच्याय दोन फरकांच्या कार्यां खातीर, दोन कार्यांच्या गुणकाराचो व्यत्पन्न हो गणकाच्या व्यत्पन्नाच्या भाजक पटीन आसा, जो भाजकाच्या व्यत्पन्नाच्या गणक पटीन वजा करचो, सगळे भाजकाच्या वर्गाकडेन विभागचें.

$$\frac{\left(x^{2}+8x^{1}+12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-6)-\left(x^{1}-6\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+8x^{1}+12)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

पोलिनोमियलाचें व्यत्पन्न हें तांच्या संज्ञांच्या व्यत्पन्नाची बेरीज आसता. खंयच्याय थीर संख्येचें व्यत्पन्न 0 आसता. हाचें व्यत्पन्न ax^{n} हें nax^{n-1} आसा.

$$\frac{\left(x^{2}+8x^{1}+12\right)x^{1-1}-\left(x^{1}-6\right)\left(2x^{2-1}+8x^{1-1}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

सोंपें करचें.

$$\frac{\left(x^{2}+8x^{1}+12\right)x^{0}-\left(x^{1}-6\right)\left(2x^{1}+8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

x^{0}क x^{2}+8x^{1}+12 फावटी गुणचें.

$$\frac{x^{2}x^{0}+8x^{1}x^{0}+12x^{0}-\left(x^{1}-6\right)\left(2x^{1}+8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

2x^{1}+8x^{0}क x^{1}-6 फावटी गुणचें.

$$\frac{x^{2}x^{0}+8x^{1}x^{0}+12x^{0}-\left(x^{1}\times 2x^{1}+x^{1}\times 8x^{0}-6\times 2x^{1}-6\times 8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

समान बेझीचे पॉवर गुणूंक, तांच्या पुरकांची बेरीज करची.

$$\frac{x^{2}+8x^{1}+12x^{0}-\left(2x^{1+1}+8x^{1}-6\times 2x^{1}-6\times 8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

सोंपें करचें.

$$\frac{x^{2}+8x^{1}+12x^{0}-\left(2x^{2}+8x^{1}-12x^{1}-48x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

समान संज्ञा एकठांय करच्यो.

$$\frac{-x^{2}+12x^{1}+60x^{0}}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

t खंयच्याय शब्दा खातीर, t^{1}=t.

$$\frac{-x^{2}+12x+60x^{0}}{\left(x^{2}+8x+12\right)^{2}}$$

0 सोडून t खंयच्याय शब्दा खातीर, t^{0}=1.

$$\frac{-x^{2}+12x+60\times 1}{\left(x^{2}+8x+12\right)^{2}}$$

t खंयच्याय शब्दा खातीर, t\times 1=t आनी 1t=t .

$$\frac{-x^{2}+12x+60}{\left(x^{2}+8x+12\right)^{2}}$$