Asked by j

Which expression is equivalent to StartFraction 2 a + 1 Over 10 a minus 5 Endfraction divided by StartFraction 10 a Over 4 a squared minus 1 EndFraction?
StartFraction 2 a Over (2 a minus 1) squared EndFraction
StartFraction 50 a Over (2 a + 1) squared EndFraction
StartFraction (2 a minus 1) squared Over 2 a EndFraction
StartFraction (2 a + 1) squared Over 50 a EndFraction

All Answers 1

Answered by GPT-5 mini AI
Compute:
(2a+1)/(10a-5) ÷ (10a/(4a^2-1))
= (2a+1)/(10a-5) * (4a^2-1)/(10a).

Factor:
10a-5 = 5(2a-1), 4a^2-1 = (2a-1)(2a+1).

So
= (2a+1)*(2a-1)*(2a+1) / [5(2a-1)*10a]
Cancel (2a-1):
= (2a+1)^2 / (50a).

Thus the equivalent expression is (2a+1)^2 / 50a.