(x+1/x^2-25) * (x+5/x^2+8x+7)
Please explain...
x+1/(x+5)(x+7)

1/(x+5)(x+7)

1/(x-5)(x+7)

1/(x-5)(x-7)

Question

(x+1/x^2-25) * (x+5/x^2+8x+7)
Please explain... 
x+1/(x+5)(x+7)

1/(x+5)(x+7)

1/(x-5)(x+7)

1/(x-5)(x-7)

jim_thompson5910 · Answer

What would x^2-25 factor to?

hint: difference of squares

blehh10 · Answer

(x+5)(x-5)

jim_thompson5910 · Answer

good

jim_thompson5910 · Answer

what would x^2+8x+7 factor to?

hint: list out all the ways to multiply to 7. Then find out which pair of factors add to 8

blehh10 · Answer

I already did this I just don't understand how to put it together.

jim_thompson5910 · Answer

tell me what x^2+8x+7 factors to

blehh10 · Answer

(x+1)(x+7)

jim_thompson5910 · Answer

yes

jim_thompson5910 · Answer

So

$$\Large \frac{x+1}{x^2-25}*\frac{x+5}{x^2+8x+7}$$

turns into

$$\Large \frac{x+1}{(x+5)(x-5)}*\frac{x+5}{(x+1)(x+7)}$$

blehh10 · Answer

So... what does that mean?

jim_thompson5910 · Answer

Multiply the terms straight across to combine the fractions

making 

$$\Large \frac{x+1}{(x+5)(x-5)}*\frac{x+5}{(x+1)(x+7)}$$

turn into

$$\Large \frac{(x+1)(x+5)}{(x+5)(x-5)(x+1)(x+7)}$$

jim_thompson5910 · Answer

Notice these (x+1) terms pair up. One in the numerator. One in the denominator

$$\Large \frac{{\color{red}{(x+1)}}(x+5)}{(x+5)(x-5){\color{red}{(x+1)}}(x+7)}$$

jim_thompson5910 · Answer

The (x+1) terms will cancel since x/x = 1 (where x is nonzero)
$$\Large \frac{{\color{red}{\cancel{(x+1)}}}(x+5)}{(x+5)(x-5){\color{red}{\cancel{(x+1)}}}(x+7)}$$

blehh10 · Answer

Ohh. Thanks I get it now. I forgot about the cancelling!

blehh10 · Answer

You also cancel (x+5)

jim_thompson5910 · Answer

After that cancellation of the (x+1) terms, we're left with this

$$\Large \frac{x+5}{(x+5)(x-5)(x+7)}$$

I'm sure you see at this point the (x+5) terms cancel as well

jim_thompson5910 · Answer

`You also cancel (x+5)`
yes correct

blehh10 · Answer

So since you helped me can I give you a medal or something? I don't know if I can?

jim_thompson5910 · Answer

to give out a medal, click on the blue "best answer" button

blehh10 · Answer

Where is that?

adrimit · Answer

the upper right corner of the comment you want to give the medal to

blehh10 · Answer

So I did it?

adrimit · Answer

yes

blehh10 · Answer

Okay thanks, I haven't really used openstudy.

jim_thompson5910 · Answer

yes @blehh10 you gave out the medal, thank you

blehh10 · Answer

Really, thank you!

adrimit · Answer

welcome to open study :)

blehh10 · Answer

Thanks!