Hey!
First, let's write the problem.
[tex]\frac{x}{x}+2=\frac{4}{5}[/tex]
Since the least common multiple is 5x, we are going to multiply by that.
[tex]\frac{x}{x}\cdot \:5x+2\cdot \:5x=\frac{4}{5}\cdot \:5x[/tex]
[tex]5x+10x=4x[/tex]
[tex]15x=4x[/tex]
Subtract 4x from both sides.
[tex]15x-4x=4x-4x[/tex]
[tex]11x=0[/tex]
Divide both sides by 11.
[tex]\frac{11x}{11}=\frac{0}{11}[/tex]
Our final answer would be,
[tex]x=0[/tex]
This tells us that this problem has no solution.
_________
Your problem may have been written like this,
[tex]\frac{x}{\left(x+2\right)}=\frac{4}{5}[/tex]
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,
[tex]x\cdot \:5=\left(x+2\right)\cdot \:4[/tex]
Apply the distributive property.
[tex]x\cdot \:5=4x+8[/tex]
Subtract 4x from both sides.
[tex]x\cdot \:5-4x=4x+8-4x[/tex]
This tells us that our final answer would be,
[tex]x=8[/tex]
Thanks!
-TetraFish
