Math Help - factoring

1. factoring

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.

2. Re: factoring

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?

3. Re: factoring

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

4. Re: factoring

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?

5. Re: factoring

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

6. Re: factoring

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

7. Re: factoring

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

8. Re: factoring

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

9. Re: factoring

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

10. Re: factoring

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

11. Re: factoring

That's better...

12. Re: factoring

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

13. Re: factoring

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 :

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