Question

How do you combine like terms in `\frac { 3x } { x ^ { 2} + 2x } + \frac { 11} { x } + \frac { 2x ^ { 2} } { x ^ { 2} - x }`?

Answer 1

`[3x]/[x(x+2)]+11/x+[2x^2]/[x(x-1)]`

`[3]/[(x+2)]+11/x+[2x]/[(x-1)]`

Find a common denominator

`[3x(x-1)+11(x+2)(x-1)+2x(x+2)x]/[x(x+2)(x-1)]`

`[3x^2-3x+11(x^2+x-2)+2x^3+4x^2]/[x(x+2)(x-1)]`

`[3x^2-3x+11x^2+11x-22+2x^3+4x^2]/[x(x+2)(x-1)]`

`[2x^3+18x^2+8x-22]/[x(x+2)(x-1)]`