Question

The solution for the equation $(\frac{1}{x+2}+\frac{1}{x+3}=\frac{2}{x+9})$ is

• A. $\frac{-33}{13}$
• B. $\frac{-23}{13}$
• C. $\frac{-43}{13}$
• D. $\frac{-53}{13}$

Answer 1

The correct option is A $\frac{-33}{13}$

$\frac{1}{x+2}+\frac{1}{x+3}=\frac{2}{x+9}$

$=\frac{1}{x+2}+\frac{1}{x+3}-\frac{2}{x+9}=0$

$=\frac{(x+3)(x+9)+(x+2)(x+9)-2(x+2)(x+3)}{(x+2)(x+3)(x+9)}=0$

$=(x^2+12x+27)+(x^2+11x+18)-2(x^2+5x+6)=0$

$=x^2+12x+27+x^2+11x+18-2x^2-10x-12=0$

$=13x+33=0$

$x=-\frac{33}{13}$

$\text{Option A is correct.}$