Question

Solve for $x$ : $\frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5}$

Answer 1

$\frac{2}{x+1}+\frac{3}{2(x-2)}=\frac{23}{5}$

$\frac{4(x-2)+3(x+1)}{2(x+1)(x-2)}=\frac{23}{5}$

$\frac{7x-5}{2x^2-2x-4}=\frac{23}{5}$

$35x-25=46x^2-46x-92$

$46x^2-81x-67=0$

Solving the above quadratic equation, we get,

$x=\frac{81\pm \sqrt{18889}}{92}$