Solve the following quadratic equation by factorization:
$\frac{1}{x\ -\ 1}\ –\ \frac{1}{x\ +\ 5}\ =\ \frac{6}{7},\ x\ ≠\ 1,\ -5$

Given:

Given quadratic equation is $\frac{1}{x\ -\ 1}\ –\ \frac{1}{x\ +\ 5}\ =\ \frac{6}{7},\ x\ ≠\ 1,\ -5$.

To do:

We have to solve the given quadratic equation by factorization.

Solution:

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

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

$7(x+5-x+1)=6(x-1)(x+5)$    (On cross multiplication)

$42=6(x^2+5x-x-5)$

$x^2+4x-5=\frac{42}{6}$

$x^2+4x-5-7=0$

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

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

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

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

$x+6=0$ or $x-2=0$

$x=-6$ or $x=2$

The roots of the given quadratic equation are $-6$ and $2$. 

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Updated on: 10-Oct-2022

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