Question

How do you simplify `(14r)/(9-r)-(2r)/(r-9)`?

Answer 1

See a solution process below:

Explanation:

To subtract these fractions we need them to be over a common denominator. Because the denominators are the "opposites" of each other we can multiple one of the fractions by the form of `1` of `-1/-1`:

`((-1)/-1 xx (14r)/(9 - r)) - (2r)/(r - 9) =>`

`(-1 xx 14r)/(-1(9 - r)) - (2r)/(r - 9) =>`

`(-14r)/(-9 + r) - (2r)/(r - 9) =>`

`(-14r)/(r - 9) - (2r)/(r - 9)`

We can now subtract the numerators of the two fractions over the common denominator:

`(-14r - 2r)/(r - 9) =>`

`((-14 - 2)r)/(r - 9) =>`

`(-16r)/(r - 9)`