Question

Solve the following equation:

$\frac{15}{x+6}-\frac{1}{x-2}=\frac{6}{x+2};x\ne 0$.

• A. $6$
• B. $3$
• C. $4$
• D. $9$

Answer 1

The correct option is C $4$

$\frac{15}{x+6}-\frac{1}{x-2}=\frac{6}{x+2}$

$\frac{15(x-2)-1(x+6)}{(x+6)(x-2)}=\frac{6}{x+2}$

$\frac{15x-30-x-6}{(x+6)(x-2)}=\frac{6}{x+2}$

$\frac{14x-36}{(x+6)(x-2)}=\frac{6}{x+2}$

$(14x-36)(x+2)=6(x+6)(x-2)$

$14x^2-36x+28x-72=6x^2+36x-12x-72$

$14x^2-8x-72=6x^2+24x-72$

$8x^2=32x$

$\therefore x=4$