Question

Can someone please simplify the complex fraction?

Answer 1

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