Dividing Complex Fractions

[myrealname]

Hi all! I'm helping my daughter with her math and it's been SO long since I've done algebra 2...

Anyhow, here is the problem:

y+3 ÷ y²+7y+12
5-y y+5

I get as far as 1 * y-5
5-y y+4

Does the 5-y cancel the y-5 and make the answer 1/y+4? I don't remember negatives being able to cancel out a positive.... But I sure could be wrong!

 

[srmichael]

I'm not sure where you got y-5 in the numerator of your simplified solution. The way I see it is like this:

\(\displaystyle \frac{y+3}{5-y}\div\frac{y^2+7y+12}{y+5}\)

Then, do the ol' Keep-Change-Flip and get

\(\displaystyle \frac{y+3}{5-y}\cdot\frac{y+5}{y^2+7y+12}\)

\(\displaystyle \frac{y+3}{5-y}\cdot\frac{y+5}{(y+3)(y+4)}\)

Cancelling out the \(\displaystyle (y+3)\) you get

\(\displaystyle \frac{1}{5-y}\cdot\frac{y+5}{y+4}\)

And that's about it. You can simplify by multiplying and getting

\(\displaystyle \frac{y+5}{(5-y)(y+4)}\)

I normally don't do the entire problem for someone, but I'm a parent too and can understand your frustration

 

[pka]

Anyhow, here is the problem:

[U]y+3[/U] ÷ [U]y[SUP]2[/SUP]+7y+12[/U] 
5-y     y+5

That equals \(\displaystyle -\dfrac{y+3}{y-5}\cdot \dfrac{y+5}{(y+3)(y+4)}\).

You can divide out \(\displaystyle y+3\)

 

[mmm4444bot]

the ol' Keep-Change-Flip

This general rule can also be taught as "dividing by a fraction is the same operation as multiplying by the reciprocal of that fraction, and we make the switch because multiplication is easier".

I normally don't do the entire problem for someone

I don't see any harm done, in this thread. The original poster shows effort (by including some work) and interest (by asking a specific question).

 

[myrealname]

JeffM is on the right track (I should have stated that we have the answer in the book, we just don't know how to get there!)

The book gives 1/(y+4) as the answer.

I understand all of the steps that JeffM put down except the last step of factoring (5-y) to make it cancel out the (y+5) and (y-5) so that my answer would be 1/(y+4). Is there another way to explain it?

Thanks!

PS I don't do the whole problem for my children either, but *I* need to understand what I am teaching them or it doesn't help them to understand...to 'walk them through the steps' so to speak

 

[myrealname]

Nope, no typo. I checked and double checked.

Yay!

Thanks again!