Question

State true or false:

If $\frac{7}{3x-4}-\frac{2}{x+2}=1$, then $x$ is $3$ or $-\frac{10}{3}$

• A. True
• B. False

Answer 1

The correct option is A True

$\frac{7}{3x-4}-\frac{2}{x+2}=1$
$7(x+2)-2(3x-4)=(3x-4)(x+2)$
$7x+14-6x+8=3x^2+6x-4x-8$
$x+22=3x^2+2x-8$
$3x^2+x-30=0$
$x=\frac{-1\pm \sqrt{1+360}}{2\times 3}$
$=\frac{-1\pm 19}{6}$
$=3,\frac{-10}{3}$