Question

Which expression is equivalent to the following complex fraction?

StartFraction x Over x minus 3 EndFraction divided by StartFraction x squared Over x squared minus 9 EndFraction
StartFraction x minus 3 Over x EndFraction
StartFraction x + 3 Over 1 EndFraction
StartFraction x + 3 Over x EndFraction
StartFraction x Over x + 3 EndFraction

Answer 1

(x/(x-3)) ÷ (x^2/(x^2-9))
= x/(x-3) * (x^2-9)/x^2
= x/(x-3) * (x-3)(x+3)/x^2
= (x+3)/x.

So the equivalent expression is (x+3)/x (with x ≠ 0, 3, −3).