factoring

**hannah2329** · September 12th 2011, 01:24 PM

I have two problems that i need help with.

the first is (5x/y)/(9z)

would you multiply by 1/9z? to get 5x/9yz?

the second is 7x^-1 + 7y^-1
6(x + y)^-1 so this one you would want to put every thing under one so the negatives would cancel out then the lcd is 7x 7y? I'm really confused on this problem.

**pickslides** · September 12th 2011, 01:42 PM

Your answer to the first question is correct.

For the second one $\displaystyle \frac{7x^{-1}+7y^{-1}}{6(x+y)^{-1}} = \frac{(7x^{-1}+7y^{-1})(x+y)}{6}$

Now expand the numerator, what do you get?

**hannah2329** · September 12th 2011, 03:20 PM

by expand do you mean like foil? or combine the like terms and add the exponents so it would be 7x+7y/6?

**pickslides** · September 12th 2011, 03:44 PM

Originally Posted by hannah2329

by expand do you mean like foil?

Yes, then combine any like terms.

Originally Posted by hannah2329

so it would be 7x+7y/6?

I don't think its that, how did you get that?

**hannah2329** · September 12th 2011, 04:03 PM

i don't know, I'm confused. if you multiply and add the exponents wouldn't it be -1+1?

**hannah2329** · September 12th 2011, 04:05 PM

so it would be 0. is the answer 1/6? I'm really lost.

**pickslides** · September 12th 2011, 05:25 PM

$\displaystyle \frac{(7x^{-1}+7y^{-1})(x+y)}{6} = \frac{7x^{-1}x+7x^{-1}y+7y^{-1}x+7y^{-1}y}{6}= \frac{7+7x^{-1}y+7y^{-1}x+7}{6}= \dots$

**hannah2329** · September 12th 2011, 05:33 PM

i got that far but i don't know how to get rid of the negatives

**pickslides** · September 12th 2011, 05:37 PM

You can factor out 7 in the numerator. Do you have to get rid of the negatives?

**hannah2329** · September 12th 2011, 05:39 PM

yea i have to get rid of the negatives so 7(y/x+x/y+2)/6

**pickslides** · September 12th 2011, 05:49 PM

That's better...

**hannah2329** · September 12th 2011, 05:55 PM

i put that in and it wasn't right. is there any way to simplify it further?

**psolaki** · September 12th 2011, 06:32 PM

Originally Posted by hannah2329

i put that in and it wasn't right. is there any way to simplify it further?

You can simplify even further and get :

$\frac{7(x+y)^2}{6xy}$

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