Adding Algebraic Fractions with Variables by: Karin

Hi Charlotte,

I'm sorry to just be getting back to you, but I've been out of town.

You have a great question! You first want to remove the variables from the denominator. Since there is an x in the denominator of both fractions, we can multiply both sides by x.

x(1/x+2/3x) = 4(x)

Distribute the x and we get:

x/x+ 2x/3x = 4x

The x in the numerator and denominator or each fraction simplify to 1 (or cancel out). Then you have:

1+2/3 = 4x

Add 1+2/3 and you get 5/3.

5/3 = 4x

To isolate x, we need to divide by 4 on both sides.

(5/3) / 4 = 4x/4

When you divide fractions, you actually multiply by the reciprocal, so we have: