Solve by factorization: `1/(x+4)-1/(x-7)=(11)/(30),\ \ x!=4,\ 7`

Explanation

Given equation is
`(1)/(x+4)-(1)/(x-7)=(11)/(30)`
`implies((x-7)-(x+4))/((x+4)(x-7))=(11)/(30)`
`implies(x-7-x-4)/(x^(2)-7x+4x-28)=(11)/(30)`
`implies(-11)/(x^(2)-3x-28)=(11)/(30)`
`implies11(x^(2)-3x-28)=-11xx30`
`impliesx^(2)-3x-28=-30`
`impliesx^(2)-3x+2=0`
`impliesx^(2)-(2+1)x+2=0`
`impliesx^(2)-2x-1x+2=0`
`impliesx(x-2)-1(x-2)=0`
`implies(x-2)(x-1)=0`
`impliesx-2=0orx-1=0`
when `x-2=0impliesx=2`
and `x-1=0impliesx=1`
Hence, 2 and 1 are roots of the equation.