Question

1/2x^-1/2 (3x+8)^1/2 - 3/2x^1/2 (3x+8)^-1/2
the answer is 4 / x^1/2 (3x+8)^1/2.
I understand x^-1/2 (3x+8)^-1/2 was factored out of the equation and rationalized to the denominator but i cannot figure our how to get the 4 in the numerator. any help would be much appreciated.

Answer 1

if you could write the question using the equation function, that would be great. it's a bit confusing reading it in text

Answer 2

\[\frac{ 1 }{ 2 }x ^{-\frac{ 1 }{ 2 }}\left( 3x+8 \right)^{\frac{ 1 }{ 2}}-\frac{ 3 }{ 2}x ^{\frac{ 1 }{ 2 }}\left( 3x+8 \right)^{\frac{ -1 }{ 2 }}\]

Answer 3

\[\frac{ 4 }{ x ^{\frac{ 1 }{ 2 }}\left( 3x+8 \right)^{\frac{ 1 }{ 2 }} }\]

Answer 4

is the answer i cannot figure out how to get the 4 in the numerator

Answer 5

i just want to ask is the 1/2 power after the x supposed to be like that in both terms? one neg and one pos?

Answer 6

yes there is a -1/2 power in two terms and a pos 1/2 power in two terms

Answer 7

the main idea of the exercise is to factor the terms completely

Answer 8

if you factor out x^-1/2 and (3x+8)^-1/2 that is how you get the denominator

Answer 9

by rationalizing you would have 1/ x^1/2 (3x+8)^1/2

Answer 10

hold on lemme write this out

Answer 11

well i got the negative version of your answer

Answer 12

actually here's a thought. i'm just putting it here, but i haven't looked over it yet but when you pull out the x^-1/2 (3x+8)^-1/2 to the front to factor out. doesn't the rest of the equation becomes [1/2 (3x+8)-3/2(x)]

Answer 13

and when you simplify that you get 1.5x+4-1.5x which leaves 4 as your numerator

Answer 14

remember when you multiply the factored stuff back in, you should get the same equation as before.

Answer 15

Thank you so much!