Thread: Quotient Rule - Factorization Question

Hi, I am not sure how the 1/2x^-1/2 was factorized out in this numerator that was derived from the quotient rule. Can some please explain.

= (x^2 + 1) (1/2x^-1/2) – x^1/2 (2x)
=1/2x^-1/2 (x^2 +1 – 4x^2)
I understand how factorization works but I am not sure what happened in this case.

Thank you.

=1/2x^-1/2 (x^2 +1 – 4x^2)

isn't correct

recall x^(1/2) = x^(-1/2) * x


(1/2x^-1/2) – x^1/2 (2x) = x^(-1/2)[ 1/2 -x (2x)]

= 1/2x^(-1/2)[1-4x^2]