Solve 1 x 4 1 x 7 11 30

Asked by admin @ 13/08/2021 in Math viewed by 357 People

Solve by factorising 1/x+4 - 1/x-7 = 11/30 ; x is not equal to -4,7

Answered by admin @ 13/08/2021

Answer:

The solution of the expression is x=2,1.

Step-by-step explanation:

Given : Expression $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}$ where $x\neq -4,7$

To find : Solve the expression by factoring?

Solution :

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

Taking LCM,

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

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

Cross multiply,

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

$(x+4)(x-7)=-30$

Multiply the term,

$x^2-7x+4x-28=-30$

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

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

Apply middle term split,

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

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

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

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

$x=2,x=1$

Therefore, The solution of the expression is x=2,1.

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