Question

How do you add or subtract `(x^2+2x)/(12x+54) - (3-x)/(8x+36)`?

Answer 1

`(x-1)/12`

Explanation:

Given: `(x^2+2x)/(12x+54) - (3-x)/(8x + 36)`

Factor both numerators and denominators:

`(x^2+2x)/(12x+54) - (3-x)/(8x + 36) = (x(x+2))/(6(2x+9)) - (3-x)/(4(2x+9))`

Find the common denominator and simplify:

`(x(x+2))/(6(2x+9))*(2/2) - (3-x)/(4(2x+9))(*3/3)`

`(2x(x+2))/(12(2x+9)) - (3 (3-x))/(12(2x+9))`

`(2x(x+2) - 3(3-x))/(12(2x+9))`

`(2x^2 + 4x - 9 +3x)/(12(2x+9))`

`(2x^2 + 7x - 9)/(12(2x+9))`

Factor the quadratic in the numerator:
`((2x + 9)(x - 1))/(12(2x+9))`

Cancel any common factors:
`(cancel((2x + 9))(x - 1))/(12cancel((2x+9)))`

`= (x-1)/12`