Question

Can someone please simplify the complex fraction?

Answer 1

$\bf \cfrac{\qquad \frac{x+3}{4x^2-16}\qquad }{\frac{2x^2+10x+12}{2x-4}}\implies \cfrac{\frac{x+3}{4(x^2-4)}}{\frac{\underline{2}(x^2+5x+6)}{\underline{2}(x-2)}}\implies \cfrac{\frac{x+3}{4(x^2-2^2)}}{\frac{x^2+5x+6}{x-2}}\implies \cfrac{\frac{x+3}{4(x-2)(x+2)}}{\frac{(x+3)(x+2)}{x-2}}$

$\bf \cfrac{\underline{x+3}}{4\underline{(x-2)}(x+2)}\cdot \cfrac{\underline{x-2}}{\underline{(x+3)}(x+2)}\implies \cfrac{1}{4(x+2)}\cdot \cfrac{1}{x+2} \\\\\\ \cfrac{1}{4(x+2)(x+2)}\implies \cfrac{1}{4(x^2+4x+4)}\implies \cfrac{1}{4x^2+16x+16}$