Solve: `(1)/((x+3))+(1)/((2x-1))=(11)/((7x+9)),xne-3,(1)/(2),(-9)/(7).`

Explanation

We have
`(1)/((x+3))+(1)/((2x-1))=(11)/((7x+9))`
`implies" "((2x-1)+(x+3))/((x+3)(2x-1))=(11)/((7x+9))implies((3x+2))/(2x^(2)+5x-3)=(11)/((7x+9))`
`implies" "(3x+2)(7x+9)=11(2x^(2)+5x-3)" "["by cross multiplication"]`
`implies" "21x^(2)+41x+18=22x^(2)+55x-33`
`implies" "x^(2)+14x-51=0impliesx^(2)+17x-3x-51=0`
`implies" "x(x+17)-3(x+17)=0implies(x+17)(x-3)=0`
`implies" "x+17=0" or "x-3=0`
`implies" "x=-17" or "x=3.`
Hence, -17 and 3 are the roots of the given equation.