Question

What is the simplified form of 3/4x+3+21/8x^2-14x-15

Answer 1

Solution:

We have been asked to find the simplified expression of

$3/4x+3+21/8x^2-14x-15=\frac{3}{4x+3} +\frac{21}{8x^2-14x-15}\\ \\ \text{We will have to make the denominator equal to add}\\ \\ \ 8x^2-14x-15=8x^2+6x-20x-15\\ \\ \ =2x(4x+3)-5(4x+3)=(4x+3)(2x-5)\\ \\ \frac{3}{4x+3} +\frac{21}{8x^2-14x-15}=\frac{3}{4x+3} +\frac{21}{(4x+3)(2x-5)}\\ \\ =\frac{3(2x-5)+21}{(4x+3)(2x-5)}\\ \\ =\frac{6x-15+21}{(4x+3)(2x-5)} \\ \\ =\frac{6x+6}{(4x+3)(2x-5)}$