4/X+3 = 7/X+9

Question

Got this on a test and couldn't figure it out. Would love some explanation on how to solve it. Thanks :D

Answer 1

4/(x+3)=7(x+9).

Cross-multiply:

4(x+9)=7(x+3).

Expand:

4x+36=7x+21.

Group likes:

36-21=7x-4x,

15=3x.

Divide both sides by 3:

5=x, which is the same as x=5.

CHECK by plugging x=5 into the original equation:

4/8=7/14=½, which confirms the equality of the two fractions.