Question

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

• A. $x=18,x=-3$
  
• B. $x=12,x=-2$
• C. $x=9,x=-2$
• D. $x=10,x=-5$

Answer 1

The correct option is B $x=12,x=-2$

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

On simplifying, we get
$\frac{5x-4(x-2)}{x(x-2)}=\frac{3}{x+6}$
$\Rightarrow \frac{x+8}{x^2-2x}=\frac{3}{x+6}$
$\Rightarrow (x+8)(x+6)=3(x^2-2x)$
$\Rightarrow x^2+14x+48=3x^2-6x$
$\Rightarrow 2x^2-20x-48=0$
$\Rightarrow x^2-10x-24=0$
$\Rightarrow x^2-12x+2x-24=0$
$\Rightarrow (x-12)(x+2)=0$
Hence, $x=12$ and $x=-2$