Question

How do you combine `(x^2)/(x+3) - 9/(x+3)`?

Answer 1

`x-3`

Explanation:

`"since the fractions have a "color(blue)"common denominator"`
`"we can subtract the numerators leaving the denominator"`

`rArrx^2/(x+3)-9/(x+3)`

`=(x^2-9)/(x+3)larrcolor(blue)"combined"`

`"this may be simplified further"`

`x^2-9" is a "color(blue)"difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`rArrx^2-9=(x-3)(x+3)`

`rArr(x^2-9)/(x+3)`

`=((x-3)cancel((x+3)))/cancel((x+3))=x-3`