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

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