Question

How do you simplify `(a^2-5a)/(3a-18)-(7a-36)/(3a-18)`?

Answer 1

`(a^2-5a)/(3a-18)-(7a-36)/(3a-18) = a/3-2`

with exclusion `a!=6`

Explanation:

Since the denominators are identical, we can start by simply subtracting the numerators:

`(a^2-5a)/(3a-18)-(7a-36)/(3a-18) = (a^2-5a-7a+36)/(3a-18)`

`color(white)((a^2-5a)/(3a-18)-(7a-36)/(3a-18)) = (a^2-12a+36)/(3a-18)`

`color(white)((a^2-5a)/(3a-18)-(7a-36)/(3a-18)) = ((a-6)(color(red)(cancel(color(black)(a-6)))))/(3(color(red)(cancel(color(black)(a-6)))))`

`color(white)((a^2-5a)/(3a-18)-(7a-36)/(3a-18)) = (a-6)/3`

`color(white)((a^2-5a)/(3a-18)-(7a-36)/(3a-18)) = a/3-2`

with exclusion `a != 6`

Note that if `a=6`, then the original expression is undefined, but the simplified one is defined. So we need to specify that `a=6` is excluded.