How do you simplify #(x^2 - x-20)/(x^2 - 3x-10) times (x^2 +7x+10)/( x^2 +4x - 5)#?

Question

Julia Adams · Accepted Answer

#=(x+4)/(x-1)#

Factorise each expression as far as possible:

#(x^2-x-20)/(x^2-3x-10) xx (x^2+7x+10)/(x^2+4x-5)#

#=((x-5)(x+4))/((x-5)(x+2))xx((x+5)(x+2))/((x+5)(x-1))#

Now cancel any common factors.

#=(cancel((x-5))(x+4))/(cancel((x-5))cancel((x+2)))xx(cancel((x+5))cancel((x+2)))/(cancel((x+5))(x-1))#

#=(x+4)/(x-1)#

Jameson Allen · Answer

undefined To simplify the expression (x^2 - x - 20)/(x^2 - 3x - 10) times (x^2 + 7x + 10)/(x^2 + 4x - 5), we can factorize the numerators and denominators separately, then cancel out any common factors.

First, let's factorize the numerators and denominators:

(x^2 - x - 20) factors to (x - 5)(x + 4)
(x^2 - 3x - 10) factors to (x - 5)(x + 2)
(x^2 + 7x + 10) factors to (x + 5)(x + 2)
(x^2 + 4x - 5) factors to (x + 5)(x - 1)

Now, we can cancel out the common factors:

((x - 5)(x + 4))/((x - 5)(x + 2)) times ((x + 5)(x + 2))/((x + 5)(x - 1))

After canceling out the common factors, we are left with:

(x + 4)/(x + 2) times (x + 2)/(x - 1)

Simplifying further, we get:

(x + 4)/(x - 1)