Question

Add or subtract. Simplify your answer. x+2/x^2−100 + 8/x^2−100
A. 1x/x−10
B. 1/x−10
C. 1x/x+10
D. x+10

What is the value of m in this equation?
Type your answer as an integer, like this: -42
1/m=2/m+7

Answer 1

$\dfrac{x+2}{x^2-100}+\dfrac{8}{x^2-100}=\dfrac{x+2+8}{x^2-100}=\dfrac{x+10}{x^2-10^2}\\\\=\dfrac{x+10}{(x+10)(x-10)}=\dfrac{1}{x-10}\to\fbox{B.}\\\\\\The\ domain:\\D:m\neq0\ and\ m\neq-7\\\\\dfrac{1}{m}=\dfrac{2}{m+7}\ \ \ \ |cross\ multiply\\\\2\cdot m=1\cdot(m+7)\\2m=m+7\ \ \ \ |subtract\ "m"\ from\ both\ sides\\\boxed{m=7}$