Question

Find the roots of the following equation.
$\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30},x\ne \{-4,7\}$

• A. $-1,-2$
• B. $-1,-3$
• C. $1,3$
• D. $1,2$

Answer 1

The correct option is D $1,2$

Simplifying, we get
$\frac{1}{x+4}+\frac{1}{x-7}=\frac{11}{30}$

$\frac{x-7-x-4}{x^2-3x-28}=\frac{11}{30}$

$-30=x^2-3x-28$
$x^2-3x+2=0$

$(x-1)(x-2)=0$
$x=1$ and $x=2$