Simplifying the expression

[spacewater]

problem
\(\displaystyle \frac{(x^2+5)(\frac{1}{2})(4x+3)^\frac{-1}{2}(4)-(4x+3)^\frac{1}{2}(2x) } {(x^2+5)^2}\)

steps I've taken
\(\displaystyle \frac{\frac{(x^2+5)(\frac{1}{2})(4)-(4x+3)(2x)}{(4x+3)^\frac{1}{2}}}{(x^2+5)^2}\)

After multiplication on the numerator...
\(\displaystyle \frac{4x^3-8x^2+4}{(4x+3)^\frac{1}{2} }\cdot \frac {1}{(x^2+5)^2}\)

Final Answer
\(\displaystyle \frac{4(x^3-2x^2+1)}{\sqrt{4x+3}(x^2+5)^2}\)

The numerator threw me off. I just don't know how to approach this kind of problem. Can someone who isn't too busy teach me the steps to solve the numerator part? thanx

 

[Denis]

When you moved the (4x + 3)^(-1/2) down as (4x + 3)^(1/2), you have it under the FULL numerator:
should be under 2(x^2 + 5) only ; apart from that, you seem to be doing OK.

Example: 3*2^(-3) + 7 = 3/2^3 + 7 : got that?

 

[spacewater]

When you moved the (4x + 3)^(-1/2) down as (4x + 3)^(1/2), you have it under the FULL numerator:
should be under 2(x^2 + 5) only ; apart from that, you seem to be doing OK.

Example: 3*2^(-3) + 7 = 3/2^3 + 7 : got that?

yeah that makes sense now thanks

 

[Deleted member 4993]

When you moved the (4x + 3)^(-1/2) down as (4x + 3)^(1/2),

It is okay here because other part is multiplied by (4x + 3)^(1/2) to get (4x+3)^(1)

you have it under the FULL numerator:
should be under 2(x^2 + 5) only ; apart from that, you seem to be doing OK.

Example: 3*2^(-3) + 7 = 3/2^3 + 7 : got that?

correct - however following is also correct:

3*2^(-3) + 7 = (3 + 7*2^3)/2^3