# 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!