Question

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

Answer 1

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.

Answer 2

Answer:

(x-7)-(x+4)/(x+4)(x-7)=11/30

x-7-x-4/x^2-7x+4x-28=11/30

-7-4/x^2-7x+4x-28=11/30

-11/x^2-3x-28=11/30

-11(30)=11(x^2-3x-28)

-330=11x^2-33x-308

11x^2-33x-308-330=0

11x^2-33+22=0

x^2-3x+2=0

x^2-2x-1x+2=0

x(x-2)-1(x-2)

(x-2). (x-1)

x-2=0. x-1=0

x=2. x=1

Step-by-step explanation:

I Hope it's helpful to you