Question

Solve for $x:\frac{5}{x-2}-\frac{3}{x+6}=\frac{4}{x}$.

Answer 1

We have,

$\frac{5}{x-2}-\frac{3}{x+6}=\frac{4}{x}$

$\frac{5\left(x+6\right)-3\left(x-2\right)}{\left(x-2\right)\left(x+6\right)}=\frac{4}{x}$

$\frac{5x+30-3x+6}{x^2+6x-2x-12}=\frac{4}{x}$

$\frac{2x+36}{x^2+4x-12}=\frac{4}{x}$

$2x^2+36x=4x^2+16x-48$

$2x^2-20x-48=0$

$2x^2-12x-8x-48=0$

$2x\left(x-6\right)-8\left(x-6\right)=0$

$\left(2x-8\right)\left(x-6\right)=0$

Hence,

We get $x=4,6$