Question

Solve the following quadratic equation by factorization , the roots are:$2,-6$
$\frac{1}{x-1}-\frac{1}{x+5}=\frac{6}{7},x\ne 1,-5$

• A. True
• B. False

Answer 1

The correct option is A True

$\frac{1}{x-1}-\frac{1}{x+5}=\frac{6}{7}$

$\Rightarrow$ $\frac{(x+5)-(x-1)}{(x-1)(x+5)}=\frac{6}{7}$

$\Rightarrow$ $\frac{x+5-x+1}{x^2+5x-x-5}=\frac{6}{7}$

$\Rightarrow$ $\frac{6}{x^2+4x-5}=\frac{6}{7}$

$\Rightarrow$ $x^2+4x-5=7$

$\Rightarrow$ $x^2+4x-12=0$

$\Rightarrow$ $x^2+6x-2x-12=0$

$\Rightarrow$ $x(x+6)-2(x+6)=0$

$\Rightarrow$ $(x+6)(x-2)=0$

$\Rightarrow$ $x+6=0$ and $x-2=0$

$\therefore$ $x=-6$ and $x=2$

$\therefore$ We can see, roots given in question are correct.