Is there a way to come to the answer that (4x+14)/(x+3) is equivalent to (2)/(x+3)+4 just using methods to look at transformations? Not using other methods like partial fraction…

Question

Is there a way to come to the answer that
`(4x+14)/(x+3)` is equivalent to
`(2)/(x+3)+4` just using methods to look at transformations? Not using other methods like partial fractions or anything.

Answer 1

You can use a bit algebraic manipulation like so

(4x+14)/(x+3)

(4x+12 + 2)/(x+3)

((4x+12) + 2)/(x+3)

(4(x+3) + 2)/(x+3)

4(x+3)/(x+3) + 2/(x+3)

4 + 2/(x+3)

2/(x+3) + 4