Write three different rational expressions that are equivalent to the expression a/a-5. State how you know the three additional equations are equivalent to a/a-5.

Question

First time taking college algebra. Need assistance before test tomorrow :)

Answer 1

Any common multiple of denominator and numerator produces the same fraction. So 2a/(2a-10) and 3a/(3a-15) produce the same fraction, for example. ax/(ax-5x) where x≠0 also produces the fraction. A less obvious one is (a^2+5a)/(a^2-25)=a(a+5)/(a^2-25), the reason being that the denominator factorises: a(a+5)/((a-5)(a+5))=a/(a-5).