Question

simplify
$\frac{1}{x+6}+\frac{1}{x-10}=\frac{3}{x-4}$ $x\ne 4,10,-6$

Answer 1

On taking L.C.M ,we get

$\frac{x-10+x+6}{(x+6)(x-10)}=\frac{3}{x-4}$

$\Rightarrow (2x-4)(x-4)=3(x+6)(x-10)$

$\Rightarrow 2x^2-8x-4x+16=3(x^2-10x+6x-60)$

$\Rightarrow 2x^2-8x-4x+16=3x^2-12x-180$

$\Rightarrow x^2=196$

$x=\pm 14$