Question

How do you simplify `(18y)/(9y+2)-(-4)/(-2-9y)`?

Answer 1

See the entire simplification process below:

Explanation:

First, multiply the second fraction in the expression by `color(red)((-1)/-1)` to put both fractions over a common denominator. We can multiply the fraction by this because it does not change the value of the fraction as `(-1)/-1 = 1`

`(18y)/(9y + 2) - (-4)/(-2 -9y)` becomes:

`(18y)/(9y + 2) - (color(red)((-1)/-1) xx (-4)/(-2 - 9y)) ->`

`(18y)/(9y + 2) - (-1 xx -4)/(-1(-2 - 9y)) ->`

`(18y)/(9y + 2) - 4/(2 + 9y) ->`

`(18y)/(9y + 2) - 4/(9y + 2)`

We can now subtract the numerators of the two fractions because they have common denominators:

`(18y - 4)/(9y + 2)`