Question

Sonji correctly added 2p+1/p-8 and 3p-3/4p and got 8p^2+4p+3p-27p+24/(p-8)(4p). What is the simplified sum?

Answer 1

`(11p^2-23p+24)/(4p(p-8))`

Explanation:

Given expression,

`(2p+1)/(p-8)+(3p-3)/(4p)`

`=(4p(2p+1)+(p-8)(3p-3))/(4p(p-8))`

`=(8p^2+4p+3p^2-24p-3p+24)/(4p(p-8))`

By combining like terms,

`=(11p^2-23p+24)/(4p(p-8))`

Since, further simplification is not possible because numerator is not the perfect square trinomial,

Hence, the required simplified sum is,

`(11p^2-23p+24)/(4p(p-8))`

Answer 2

The simplified sum is
`(11p^(2)-23p+24)/((p-8)4p)`

Step-by-step explanation:

we have

`(2p+1)/(p-8)+(3p-3)/(4p)=(4p(2p+1)+(p-8)(3p-3))/((p-8)4p)\\ \\=(8p^(2)+4p+3p^(2)-3p-24p+24)/((p-8)4p)\\ \\ =(11p^(2)-23p+24)/((p-8)4p)`