Question

How do you combine `(x+2)/(x-5)+(x-12)/(x-5)`?

Answer 1

`(2x-10)/(x+5)`

Explanation:

`(x+2)/(x-5)` `+` `(x-12)/(x-5)`

Since both denominators are the same, just combine the fraction, like so,

`((x+2)+(x-12))/(x-5)`

Open up the brackets,

`(x+2+x-12)/(x-5)`
`(2x-10)/(x+5)`

Answer 2

`2`

Explanation:

Before we can add/subtract fractions we require them to have a `color(blue)"common denominator"`

These fractions have a common denominator ( x - 5) so we can add the numerators, leaving the denominator as it is.

`rArr(x+2+x-12)/(x-5)`

`=(2x-10)/(x-5)`

The numerator can be simplified by taking out a `color(blue)"common factor"`

`rArr(2x-10)/(x-5)=(2(cancel(x-5))^1)/cancel(x-5)^1`

`color(blue)"cancelling" " a common factor of " (x-5)`

`=2`

Answer 3

`2`

Explanation:

`(x+2)/(x-5)+(x-12)/(x-5)`

`:.=(x+2+x-12)/(x-5)`

`:.=(2x-10)/(x-5)`

`:.=(2cancel((x-5))^color(red)1)/cancel((x-5))^color(red)1`

`:.=2`