B Factoring algebraic expressions contaning fractions

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1. May 29, 2016

leighflix

http://imgur.com/RNsBBoO (image)

Can someone elaborate as to how he factored this? The textbook provided nothing else about factoring algebraic expressions with fractions than this image.It avoided fractions in factoring like a plague I guess.

I understand the 3rd step to put the (x + 1)^(3/4) on the bottom since the exponent was negative. However I have absolutely no idea how the former 2 steps were possible.

2. May 29, 2016

Staff: Mentor

Do you agree that $(x + 1)^{1/4}$ in the first step is the same as (equal to) $(x + 1)^{-3/4}(x + 1)$ in the second step?
The purpose of doing this was to get a common factor of $(x + 1)^{-3/4}$, and then using the distributive law.

3. May 29, 2016

leighflix

I have no idea how (x + 1)^(1/4) = (x + 1)^(-3/4) * (x + 1)

EDIT: Ok, I get how it is equilavent

4. May 29, 2016

leighflix

In step 1 & 2, did he group factor?

(2x + 1)(x + 1)^(-3/4) = (2x+1) / (x + 1)^(3/4)

EDIT: OK no, he didn't group factor, he basically just added x and (x+1).
I understand now, thanks.

5. May 29, 2016

SteamKing

Staff Emeritus
It's also equivalent.

6. May 29, 2016

SteamKing

Staff Emeritus
Naw. With a negative exponent, you can just re-write it so that term appears in the denominator.

You know: $a ⋅ b^{-n} = \frac{a}{b^n}$

7. May 29, 2016

leighflix

Yea, that was what I was thinking. Simply just add similar to adding fractions, since they have the same denominator, just add both numerators.

8. May 29, 2016

SteamKing

Staff Emeritus
You got it.

9. May 29, 2016

leighflix

Thanks both of you!