# How do I solve an equation with a variable in the numerator?

1. ### AVReidy

49
1. The problem statement, all variables and given/known data

I just missed a 16-point question on a quiz because I didn't know how to separate the variable. It was an absolute value equation, but I just need to know how to deal with a variable in a fraction. Here's what it looked like:

2. Relevant equations

(5x+10)/2 = 20

3. The attempt at a solution
I tried multiplying everything by the denominator, but I'm not sure if or why that works. Any help would be greatly appreciated, thanks!

### Staff: Mentor

Multiplying by denominator should work. You can do anything that doesn't change the equality - that means adding, subtracting, multiplying or dividing both sides of the equation by the same thing.

Or you could write the fraction as $\frac {5x}{2} + \frac {10}{2}$.

49
Thanks!

4. ### J2R

2
The easiest way is to multiply both sides of the equation by the denominator. The reason why this works is because it doesn't change the equality.

(5x+10)/2 = 20
5x+10 = 40
5x = 30
x = 6

Even if the variable was in the denominator, you can still solve for the variable using the same steps.

2/(5x+10) = 20
2 = 100x + 200
-198 = 100x
-198/100 = x
x = -99/50