Question

Find the number of real solution to the rational equation
$\frac{2}{(x+1)}-\frac{1}{(x-2)}=-1$ find value of $x^2$

Answer 1

Solve the given equation as follows:

$\frac{2}{(x+1)}-\frac{1}{(x-2)}=-1$

$\Rightarrow 2(x-2)-(x+1)=-\left[\right(x+1\left)\right(x-2\left)\right]$

$\Rightarrow 2x-4-x-1=-[x^2-x-2]$

$\Rightarrow x-5=-x^2+x+2$

$\Rightarrow x^2-7=0$

$\Rightarrow x^2=7$

$\Rightarrow x=\pm \sqrt{7}$