Factoring algebraic expressions contaning fractions

In summary, the conversation discusses how to factor an algebraic expression with fractions. The first step involves rewriting a term with a positive exponent as a term with a negative exponent and multiplying it with another term. The second step is to get a common factor by using the distributive law. Finally, the third step is to put the term with the negative exponent in the denominator.
  • #1
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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.
 
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  • #2
leighflix said:
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.
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.
 
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  • #3
Mark44 said:
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.

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

EDIT: Ok, I get how it is equilavent
 
  • #4
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
leighflix said:
I have no idea how (x + 1)^(1/4) = (x + 1)^(-3/4) * (x + 1)

EDIT: Ok, I get how it is equilavent
It's also equivalent. :wink:
 
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  • #6
leighflix said:
In step 1 & 2, did he group factor?

(2x + 1)(x + 1)^(-3/4) = (2x+1) / (x + 1)^(3/4)
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
SteamKing said:
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}##
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
leighflix said:
Yea, that was what I was thinking. Simply just add similar to adding fractions, since they have the same denominator, just add both numerators.
You got it.
 
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  • #9
Thanks both of you! :smile:
 

1. How do you factor algebraic expressions containing fractions?

To factor algebraic expressions containing fractions, first simplify the fractions by finding the common factors in the numerator and denominator. Then, factor the remaining polynomial using methods such as grouping, difference of squares, or the quadratic formula.

2. Can fractions be factored out of an algebraic expression?

Yes, fractions can be factored out of an algebraic expression. This is done by finding the greatest common factor (GCF) of the coefficients and variables in the expression, and factoring it out of each term.

3. What is the purpose of factoring algebraic expressions containing fractions?

The purpose of factoring algebraic expressions containing fractions is to simplify the expression and make it easier to work with. It can also help in solving equations and identifying patterns in the expression.

4. Are there any special cases when factoring algebraic expressions containing fractions?

Yes, there are a few special cases when factoring algebraic expressions containing fractions. These include expressions with a difference of squares, expressions with a perfect square trinomial, and expressions with a perfect cube trinomial.

5. Can factoring algebraic expressions containing fractions be used to solve equations?

Yes, factoring algebraic expressions containing fractions can be used to solve equations. It can help in simplifying the equation and identifying possible solutions. However, it may not always be the most efficient method and other techniques such as the quadratic formula may be needed.

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