Question

Is there a way to come to the answer that tle="\frac{4x+14}{x+3}" alt="\frac{4x+14}{x+3}" align="absmiddle" class="latex-formula"> is equivalent to $\frac{2}{x+3}+4$ 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