The problem asks to solve the fractional equation $\frac{2x}{2x+5} = \frac{3}{4} - \frac{7}{4x+10}$.

1. Problem Description

The problem asks to solve the fractional equation $\frac{2x}{2x+5} = \frac{3}{4} - \frac{7}{4x+10}$.

2. Solution Steps

First, note that $4x + 10 = 2(2x+5)$. Thus, the common denominator will be $4(2x+5)$. We must also note that $x \neq -\frac{5}{2}$, since this value would make the denominator zero.

Multiplying both sides of the equation by $4(2x+5)$, we have

$4(2x) = 3(2x+5) - 2(7)$

$8x = 6x + 15 - 14$

$8x = 6x + 1$

$8x - 6x = 1$

$2x = 1$

$x = \frac{1}{2}$

Now we check our answer:

$\frac{2(\frac{1}{2})}{2(\frac{1}{2})+5} = \frac{1}{1+5} = \frac{1}{6}$

$\frac{3}{4} - \frac{7}{4(\frac{1}{2})+10} = \frac{3}{4} - \frac{7}{2+10} = \frac{3}{4} - \frac{7}{12} = \frac{9}{12} - \frac{7}{12} = \frac{2}{12} = \frac{1}{6}$

Since $\frac{1}{6} = \frac{1}{6}$, our solution is correct.

3. Final Answer

x = 1/2