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

Simplified expression is
`(9p^(2)+10p+10)/(3p(p-2))`

Explanation:

In this question the two fractions are
`(4p+3)/(p-2)` and
`(3p+5)/(3p)`

Now Henry subtracts first fraction from the second.

`=(4p+3)/(p-2)-(3p+5)/(3p)`

`=((4p+3)3p-(3p+5)(p-2))/(3p(p-2))`

`=(12p^(2)+9p-(3p^(2)+5p-6p-10))/(3p(p-2))`

`=(12p^(2)+9p-3p^(2)+p+10)/(3p(p-2))`

`=(9p^(2)+10p+10)/(3p(p-2))`

So the simplified difference is
`(9p^(2)+10p+10)/(3p(p-2))`