Question

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

Answer 1

Hey!

First, let's write the problem.

`(x)/(x)+2=(4)/(5)`
Since the least common multiple is 5x, we are going to multiply by that.

`(x)/(x)\cdot \:5x+2\cdot \:5x=(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.

`(11x)/(11)=(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,

`(x)/(\left(x+2\right))=(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