Solve the following quadratic equation by factorization:
$\frac{1}{x\ +\ 4}\ –\ \frac{1}{x\ -\ 7}\ =\ \frac{11}{30},\ x\ ≠\ 4,\ 7$

Given:

Given quadratic equation is $\frac{1}{x\ +\ 4}\ –\ \frac{1}{x\ -\ 7}\ =\ \frac{11}{30},\ x\ ≠\ 4,\ 7$.

To do:

We have to solve the given quadratic equation by factorization. 

Solution:

$\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}$

$\frac{1(x-7)-1(x+4)}{(x+4)(x-7)}=\frac{11}{30}$

$30(x-7-x-4)=11(x+4)(x-7)$    (On cross multiplication)

$30(-11)=11(x^2-7x+4x-28)$

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

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

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

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

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

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

$x-1=0$ or $x-2=0$

$x=1$ or $x=2$

The roots of the given quadratic equation are $1$ and $2$.  

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Updated on: 10-Oct-2022

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