Question

Add or subtract. Simplify your answer. 5x+10/x^2−16 + 10/x^2−16
A. 5x/x−4
B. -x
C. 5/x−4
D. 5x+20/x^2−16

Add. Simplify your answer. 6x/5x^2 + 4x/5x^2
A. 2x/5x
B. 2/x
C. 2/x^2
D. 2x

Answer 1

$\dfrac{5x+10}{x^2-16} + \dfrac{10}{x^2-16}=\dfrac{5x+10+10}{x^2-16}=\dfrac{5x+20}{x^2-16}\\\\\dfrac{5x+20}{x^2-16}=\dfrac{5(x+4)}{x^2-4^2}=\dfrac{5(x+4)}{(x-4)(x+4)}=\dfrac{5}{x-4}\to\fbox{C.}\\\\used:a^2-b^2=(a-b)(a+b)\\\\\dfrac{6x}{5x^2}+\dfrac{4x}{5x^2}=\dfrac{10x}{5x^2}=\dfrac{2x}{x^2}=\dfrac{2}{x}\to\fbox{B.}$