सोडोवचें 1/x^2-1-2/x^2+3x-4+1/x^2-2x-3

$$\frac { 1 } { x ^ { 2 } - 1 } - \frac { 2 } { x ^ { 2 } + 3 x - 4 } + \frac { 1 } { x ^ { 2 } - 2 x - 3 }$$

मूल्यांकन करचें

$$\frac{2\left(4x-5\right)}{\left(x-3\right)\left(x+4\right)\left(x^{2}-1\right)}$$

संक्षिप्त समाधान पांवडे

x^{2}-1 गुणकपद काडचें. x^{2}+3x-4 गुणकपद काडचें.

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

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

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

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

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

x+4-2\left(x+1\right) त गुणाकार करचे.

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

x+4-2x-2 त समान शब्द एकठांय करचे.

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

x^{2}-2x-3 गुणकपद काडचें.

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

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

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

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

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

\left(-x+2\right)\left(x-3\right)+\left(x-1\right)\left(x+4\right) त गुणाकार करचे.

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

-x^{2}+3x+2x-6+x^{2}+4x-x-4 त समान शब्द एकठांय करचे.

$$\frac{8x-10}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}$$

\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right) विस्तारीत करचो.

$$\frac{8x-10}{x^{4}+x^{3}-13x^{2}-x+12}$$

w.r.t. x चो फरक काडचो

$$\frac{2\left(43-130x+67x^{2}+12x^{3}-12x^{4}\right)}{\left(\left(x-3\right)\left(x+4\right)\left(x^{2}-1\right)\right)^{2}}$$