# Thread: How to multiply algebraic fractions?

1. ## How to multiply algebraic fractions?

x+1/3 * 3x+3/2

As I would do with a normal fraction (I was told to treat algebraic fractions as normal ones) I would multiply the numerator and denominator to get;

(x+1)(3x+3)/6

My answer was wrong. Why? And how do you do it? Step by step would be appreciated.

2. ## Re: How to multiply algebraic fractions?

To be clear, your oiginal equation i:

$\displaystyle \frac {x+1} 3 \times \frac {3x+3} 2$

$\displaystyle \frac {x+1} 3 \times \frac {3x+3} 2 = \frac {(x+1)(3x+3)} 6$

but note that it can be simplified: $\displaystyle \frac {(x+1)(3x+3)} 6 = \frac {(x+1)3(x+1)} 6= \frac {(x+1)^2} 2$

What answer did they give you?

3. ## Re: How to multiply algebraic fractions?

The one you arrived on, the simplification.
Hmm, where did the 3 go and why did the denominator turn into 2?
Thanks a lot!

4. ## Re: How to multiply algebraic fractions?

Originally Posted by Ashir
Hmm, where did the 3 go and why did the denominator turn into 2?
Thanks a lot!
Simplifying fractions - the 3's in the numerator and denominator cancel out:

$\displaystyle \frac {(x+1)(3x+3)} 6 = \frac {(x+1)3(x+1)} 6= \frac {3(x+1)^2} { 3 \times 2} = \frac {(x+1)^2} 2$

5. ## Re: How to multiply algebraic fractions?

Ah, right. Thanks!
Is there a way for me to tell if I should have factorize the bracket, because I didn't know I should have factorized 3x+3.

6. ## Re: How to multiply algebraic fractions?

In general you want to get rid of common factors that are in both numerator and denominator. As for factoring - it's best to group like terms when you can. Hence 3(x+1) is a better representation than 3x+3.

7. ## Re: How to multiply algebraic fractions?

What do you mean by 'group like terms'? How did you do this here?

8. ## Re: How to multiply algebraic fractions?

The expression 3x+3 has the number '3' in it twice. So we say that 3 and 3x have "like terms," and we can pull the 3 out so it appears only once: 3x+3 = 3(x+1).

9. ## Re: How to multiply algebraic fractions?

I know what like terms are but how is that grouping if you extracted the 3? Isn't that the opposite?

10. ## Re: How to multiply algebraic fractions?

Actually I got it now, you're grouping the x+1's. Thanks for the help!