# Multiplying Rational Expressions

• Apr 10th 2008, 05:04 PM
spikeymikey
Multiplying Rational Expressions
3x+6
_______ *
X^2-4

x^2-2x
________
9

*the x^2 cancel our right?
*do I factor 3x + 6 into 3(x+2)?
Can someonw please walk me through this?
• Apr 10th 2008, 05:13 PM
TheEmptySet
Quote:

Originally Posted by spikeymikey
3x+6
_______ *
X^2-4

x^2-2x
________
9

*the x^2 cancel our right?
*do I factor 3x + 6 into 3(x+2)?
Can someonw please walk me through this?

We need to factor before we reduce

$\displaystyle \frac{3x+6}{x^2-4} \cdot \frac{x^2-2x}{9} \iff \frac{3(x+2)}{(x-2)(x+2)} \cdot \frac{x(x-2)}{9}$

reducing the above we get

$\displaystyle \frac{3(x+2)}{(x-2)(x+2)} \cdot \frac{x(x-2)}{9}=\frac{x}{3}$
• Apr 10th 2008, 05:13 PM
Mathstud28
Ok
Quote:

Originally Posted by spikeymikey
3x+6
_______ *
X^2-4

x^2-2x
________
9

*the x^2 cancel our right?
*do I factor 3x + 6 into 3(x+2)?
Can someonw please walk me through this?

IF the first problem is supposed to be $\displaystyle \frac{3x+6}{x^2-4}$...then you do the following...factor top and bottom to get $\displaystyle \frac{3(x+2)}{(x+2)(x-2)}$...cancel the $\displaystyle x+2$ to get $\displaystyle \frac{3}{x-2}$
• Apr 10th 2008, 05:24 PM
spikeymikey
Quote:

Originally Posted by TheEmptySet
We need to factor before we reduce

$\displaystyle \frac{3x+6}{x^2-4} \cdot \frac{x^2-2x}{9} \iff \frac{3(x+2)}{(x-2)(x+2)} \cdot \frac{x(x-2)}{9}$

reducing the above we get

$\displaystyle \frac{3(x+2)}{(x-2)(x+2)} \cdot \frac{x(x-2)}{9}=\frac{x}{3}$

Thank you
• Apr 10th 2008, 05:33 PM
spikeymikey
So for....
x^2+6x+5 over 3x^2+3x Mutiplied by x^2-x-20 over x^2-25

I got a final result of 1 over 3x.....is that correct?
• Apr 10th 2008, 05:40 PM
TheEmptySet
sorry :(
Quote:

Originally Posted by spikeymikey
So for....
x^2+6x+5 over 3x^2+3x Mutiplied by x^2-x-20 over x^2-25

I got a final result of 1 over 3x.....is that correct?

$\displaystyle \frac{x^2+6x+5}{3x^2+3x} \cdot \frac{x^2-x-20}{x^2-25} \iff \frac{(x+1)(x+5)}{3x(x+1)} \cdot \frac{(x-5)(x+4)}{(x-5)(x+5)}= \frac{(x+4)}{3x}$
• Apr 10th 2008, 05:44 PM
spikeymikey
Quote:

Originally Posted by TheEmptySet
$\displaystyle \frac{x^2+6x+5}{3x^2+3x} \cdot \frac{x^2-x-20}{x^2-25} \iff \frac{(x+1)(x+5)}{3x(x+1)} \cdot \frac{(x-5)(x+4)}{(x-5)(x+5)}= \frac{(x+4)}{3x}$

ok I see where I made the mistake
• Apr 10th 2008, 05:47 PM
spikeymikey
I need help with one more....

7x^3*y^4 over 6xy DIVIDED by 14x^2*y^2 over 36x^2y
• Apr 11th 2008, 05:15 AM
earboth
Quote:

Originally Posted by spikeymikey
I need help with one more....

7x^3*y^4 over 6xy DIVIDED by 14x^2*y^2 over 36x^2y

Do yourself and do us a favor and start a new thread if you have a new problem to solve.