The trick is to split items: divide four scores into two items, such as (x+5)/x-5 = (x-5+ 10)/(x-5).

=(x-5)/(x-5)+ 10/(x-5)

= 1+ 10/(x-5)

Similarly: (x-6)/(x+6) =1-12/(x+6)

(x+4)/(x-4)= 1+8/(x-4)

(x-7)/(x+7)= 1- 14/(x+7)

So the original equation is:

[ 1+ 10/(x-5)]-[ 1- 12/(x+6)]

10/(x-5)+ 12/(x+6)= 8/(x-4)+ 14/(x+7)

5/(x-5)+6/(x+6)=4/(x-4)+7/(x+7)

Then separate the two sides of the equation.

[5(x+6)+6(x-5)]/(x-5)(x+6)=[4(x+7)+(7(x-4)]/(x-4)(x+7)

1 1x/(x^2+x-30)= 1 1x/(x^2+3x-28)

1 1x(x^2+3x-28)= 1 1x(x^2+x-30)

1 1x(x^2+3x-28)- 1 1x(x^2+x-30)=0

1 1x(x^2+3x-28-x^2-x+30)=0

1 1x(2x+2)=0

x(x+ 1)=0

So x 1=0, x2=- 1.

It is verified that X 1 = 0 and X2 =- 1 are the solutions of the original fractional equation.

Do you understand?