Answer
Solving algebraically and graphically, we get the solution $x=-4$.
Work Step by Step
Solve algebraically:
$\frac{4}{x+2}-\frac{6}{2x}=\frac{5}{2x+4}$ (Multiply by $2x(x+2)$)
$8x-6(x+2)=5x$
$8x-6x-12=5x$
$2x-12=5x$ (Add with $12-5x$)
$-3x=12$
$x=\frac{12}{-3}$
$x=-4$
Solve graphically:
We sketch the graphs of $y_1=\frac{4}{x+2}-\frac{6}{2x}$ and $y_2=\frac{5}{2x+4}$ as shown below.
We can see that both intersect at $x=-4$.
So, the solution is $x=-4$.
