Question

find the roots of 1/x+4-1/x-7=11/30 , x is not equal to-4,7

Answer 1

1/(x+4) - 1/(x-7)=11/30
taking cross multiplying on LHS
(x-7-x-4)/(x^2-3x-28)=11/30
-11/(x^2-3x-28)=11/30
dividing 11 on both sides
-1/(x^2-3x-28)=1/30
cross multiplying
-30= x^2-3x-28
x^2-3x+2=0
on solving
x=1,2