Question

solve the problem
$\frac{3}{x + 1} - \frac{2}{x - 1} = \frac{5}{ {x}^{2} - 1}$
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Answer 1

begin{aligned}f'(x)&={\frac {(x^{2}-x+1)(2x+1)-(2x-1)(x^{2}+x+1)}{(x^{2}-x+1)^{2}}}\\&={\frac {2x^{3}-2x^{2}+2x+x^{2}-x+1-2x^{3}-2x^{2}-2x+x^{2}+x+1}{(x^{2}-x+1)^{2}}}\\&={\frac

Answer 2

Answer:

$x=10$

Step-by-step explanation:

As we have given in the question  there is a quadratic equation which is

$\dfrac{3}{x+1}-\dfrac{2}{x-1}=\dfrac{5}{x^{2}-1 }$

First, we solve the L.H.S by taking lcm of denominator

$\dfrac{3\times[x-1]-2[x+1]}{x^{2}-1}$

In denominator we use an identity of

$[a+b][a-b]=a^{2}-b^{2}$

Now the next step would be

$3[x-1]-2[x+1]=5$ ( As the denominator, will cancel down)

$3x-3-2x-2=5$

$x-5=5$

So the final answer would be

$x=10$