How do you multiply #1/(x^2-25) - (x+5)/(x^2-4x-5)#?

Question

1539 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-19T18:35:46

#=>1/((x-5)^2(x+1))#

I'm guessing that means you aren't subtracting, you meant to put a multiplication sign as follows:

#(1)/(x^2-25) * (x+5)/(x^2-4x-5)#

First, you would factor:

#(1)/((x+5)(x-5))*(x+5)/((x-5)(x+1))#

We see some terms cancel if they are both in the numerator and denominator:

#(1)/(cancel((x+5))(x-5))*cancel(x+5)/((x-5)(x+1))#

This gives us:

#1/(x-5)*1/((x-5)(x+1))#

Which simplifies to:

#=>1/((x-5)^2(x+1))#