सोडोवचें x^2+x/x^2-25+x^2-1/x^2+11x+30

$$\frac { x ^ { 2 } + x } { x ^ { 2 } - 25 } + \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 11 x + 30 }$$

मूल्यांकन करचें

$$\frac{\left(x+1\right)\left(2x^{2}+5\right)}{\left(x+6\right)\left(x^{2}-25\right)}$$

संक्षिप्त समाधान पांवडे

x^{2}-25 गुणकपद काडचें. x^{2}+11x+30 गुणकपद काडचें.

$$\frac{x^{2}+x}{\left(x-5\right)\left(x+5\right)}+\frac{x^{2}-1}{\left(x+5\right)\left(x+6\right)}$$

ऍक्सप्रेशन जमा करूंक वा वजा करूंक, तांचे डिनोमिनेटर तसोच दवरूंक विस्तारावचें. \left(x-5\right)\left(x+5\right) आनी \left(x+5\right)\left(x+6\right) चो किमान सामान्य गुणाकार आसा \left(x-5\right)\left(x+5\right)\left(x+6\right). \frac{x+6}{x+6}क \frac{x^{2}+x}{\left(x-5\right)\left(x+5\right)} फावटी गुणचें. \frac{x-5}{x-5}क \frac{x^{2}-1}{\left(x+5\right)\left(x+6\right)} फावटी गुणचें.

$$\frac{\left(x^{2}+x\right)\left(x+6\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}+\frac{\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

\frac{\left(x^{2}+x\right)\left(x+6\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} आनी \frac{\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर जो़डून तांची बेरीज करची.

$$\frac{\left(x^{2}+x\right)\left(x+6\right)+\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

\left(x^{2}+x\right)\left(x+6\right)+\left(x^{2}-1\right)\left(x-5\right) त गुणाकार करचे.

$$\frac{x^{3}+6x^{2}+x^{2}+6x+x^{3}-5x^{2}-x+5}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

x^{3}+6x^{2}+x^{2}+6x+x^{3}-5x^{2}-x+5 त समान शब्द एकठांय करचे.

$$\frac{2x^{3}+2x^{2}+5x+5}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

\left(x-5\right)\left(x+5\right)\left(x+6\right) विस्तारीत करचो.

$$\frac{2x^{3}+2x^{2}+5x+5}{x^{3}+6x^{2}-25x-150}$$

विस्तार करचो

$$\frac{2x^{3}+2x^{2}+5x+5}{\left(x+6\right)\left(x^{2}-25\right)}$$

संक्षिप्त समाधान पांवडे

x^{2}-25 गुणकपद काडचें. x^{2}+11x+30 गुणकपद काडचें.

$$\frac{x^{2}+x}{\left(x-5\right)\left(x+5\right)}+\frac{x^{2}-1}{\left(x+5\right)\left(x+6\right)}$$

ऍक्सप्रेशन जमा करूंक वा वजा करूंक, तांचे डिनोमिनेटर तसोच दवरूंक विस्तारावचें. \left(x-5\right)\left(x+5\right) आनी \left(x+5\right)\left(x+6\right) चो किमान सामान्य गुणाकार आसा \left(x-5\right)\left(x+5\right)\left(x+6\right). \frac{x+6}{x+6}क \frac{x^{2}+x}{\left(x-5\right)\left(x+5\right)} फावटी गुणचें. \frac{x-5}{x-5}क \frac{x^{2}-1}{\left(x+5\right)\left(x+6\right)} फावटी गुणचें.

$$\frac{\left(x^{2}+x\right)\left(x+6\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}+\frac{\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

\frac{\left(x^{2}+x\right)\left(x+6\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} आनी \frac{\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)} चे समान डिनोमिनेटर आशिल्ल्यान, तांचे न्युमरेटर जो़डून तांची बेरीज करची.

$$\frac{\left(x^{2}+x\right)\left(x+6\right)+\left(x^{2}-1\right)\left(x-5\right)}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

\left(x^{2}+x\right)\left(x+6\right)+\left(x^{2}-1\right)\left(x-5\right) त गुणाकार करचे.

$$\frac{x^{3}+6x^{2}+x^{2}+6x+x^{3}-5x^{2}-x+5}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

x^{3}+6x^{2}+x^{2}+6x+x^{3}-5x^{2}-x+5 त समान शब्द एकठांय करचे.

$$\frac{2x^{3}+2x^{2}+5x+5}{\left(x-5\right)\left(x+5\right)\left(x+6\right)}$$

\left(x-5\right)\left(x+5\right)\left(x+6\right) विस्तारीत करचो.

$$\frac{2x^{3}+2x^{2}+5x+5}{x^{3}+6x^{2}-25x-150}$$