Question

X/x+2 = 4/5. Solve for x.

Answer 1

Hey!

First, let's write the problem.
$\frac{x}{x}+2=\frac{4}{5}$
Since the least common multiple is 5x, we are going to multiply by that.
$\frac{x}{x}\cdot \:5x+2\cdot \:5x=\frac{4}{5}\cdot \:5x$
$5x+10x=4x$
$15x=4x$
Subtract 4x from both sides.
$15x-4x=4x-4x$
$11x=0$
Divide both sides by 11.
$\frac{11x}{11}=\frac{0}{11}$

Our final answer would be,
$x=0$

This tells us that this problem has no solution.

_________

Your problem may have been written like this, 
$\frac{x}{\left(x+2\right)}=\frac{4}{5}$
If so, there's a totally different solution, which is why important to include parenthesis. Let's simplify it.
Cross multiply. It would look something like this,
$x\cdot \:5=\left(x+2\right)\cdot \:4$
Apply the distributive property.
$x\cdot \:5=4x+8$
Subtract 4x from both sides.
$x\cdot \:5-4x=4x+8-4x$
This tells us that our final answer would be,
$x=8$

Thanks!
-TetraFish

Answer 2

X/x+2 = 4/5

5x = 4x + 8

5x - 4x = 8

x= 8