Chapter 3 - Section 3.2 - The Product and Quotient Rules - 3.2 Exercises - Page 188: 8

$G'(x)=\dfrac{2x^{2}+2x+4}{(2x+1)^{2}}$

$G(x)=\dfrac{x^{2}-2}{2x+1}$ Differentiate using the quotient rule $G'(x)=\dfrac{(2x+1)(x^{2}-2)'-(x^{2}-2)(2x+1)'}{(2x+1)^{2}}=\dfrac{(2x+1)(2x)-(x^{2}-2)(2)}{(2x+1)^{2}}=...$ Evaluate the product in the numerator $...=\dfrac{4x^{2}+2x-2x^{2}+4}{(2x+1)^{2}}=\dfrac{2x^{2}+2x+4}{(2x+1)^{2}}$ $G'(x)=\dfrac{2x^{2}+2x+4}{(2x+1)^{2}}$