Adding Algebraic Fractions with Variables

by Charlotte
(Denton, TX)

I am struggling with this problem. 1/x + 2/3x = 4. The answer is 5/12. How do you come up with this answer?

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Jul 18, 2011
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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:

(5/3)(1/4) = x
5/12 = x

I hope this helps!

Karin

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