`(x+2)/(x-4)+2/x+(5x)/(3x-1)` Perform the indicated operation(s) and simplify

`(x+2)/(x-4)+2/x+(5x)/(3x-1)`

LCD of the expression is `x(x-4)(3x-1)`

`=(x(3x-1)(x+2)+2(x-4)(3x-1)+5x(x)(x-4))/(x(x-4)(3x-1))`

Expand the terms in the numerator and combine the like terms,

`=(x(3x^2+6x-x-2)+2(3x^2-x-12x+4)+5x^2(x-4))/(x(x-4)(3x-1))`

`=(x(3x^2+5x-2)+2(3x^2-13x+4)+5x^3-20x^2)/(x(x-4)(3x-1))`

`=(3x^3+5x^2-2x+6x^2-26x+8+5x^3-20x^2)/(x(x-4)(3x-1))`

`=(3x^3+5x^3+5x^2+6x^2-20x^2-2x-26x+8)/(x(x-4)(3x-1))`

`=(8x^3-9x^2-28x+8)/(x(x-4)(3x-1))`

Comments

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