Question

Henry correctly subtracted 3p+5/3p from 4p+3/p-2 and got 12p2+9p-3p2+p10/(p-2)(3p). What is the simplified difference?

Answer 1

Answer:

Simplified expression is $\frac{9p^{2}+10p+10}{3p(p-2)}$

Step-by-step explanation:

In this question the two fractions are $\frac{4p+3}{p-2}$ and $\frac{3p+5}{3p}$

Now Henry subtracts first fraction from the second.

$=\frac{4p+3}{p-2}-\frac{3p+5}{3p}$

$=\frac{(4p+3)3p-(3p+5)(p-2)}{3p(p-2)}$

$=\frac{12p^{2}+9p-(3p^{2}+5p-6p-10)}{3p(p-2)}$

$=\frac{12p^{2}+9p-3p^{2}+p+10}{3p(p-2)}$

$=\frac{9p^{2}+10p+10}{3p(p-2)}$

So the simplified difference is $\frac{9p^{2}+10p+10}{3p(p-2)}$