How do you simplify #[(x^3 - 1)/(x + 4)][(2x - 7)/(x^2 + 3x + 1)]#?

1 Answer
Nov 20, 2017

Answer:

#(2x^4 - 7x^3 - 2x + 7)/(x^3 + 7x^2 + 13x + 4)#

Explanation:

We multiply the numerators with numerators and denominators with denominators.

First, let's look at the numerators.

We multiply the numerators like this:
#(x^3-1)(2x-7)# and now we need to simplify using the rainbow, FOIL, box method, or whatever way you want to do it.

#x^3 * 2x = 2x^4#

#x^3 * -7 = -7x^3#

#-1 * 2x = -2x#

#-1 * -7 = 7#

So if we put them all together, we will get #2x^4 - 7x^3 - 2x + 7#.


Now multiply the denominators:
#(x + 4)(x^2 + 3x + 1)#

#x * x^2 = x^3#

#x * 3x = 3x^2#

#x * 1 = x#

#4 * x^2 = 4x^2#

#4 * 3x = 12x#

#4 * 1 = 4#

Again, let's put them all together, and we get #x^3 + 3x^2 + x + 4x^2 + 12x + 4#

We still have to combine the "like terms":
#x^3 + 7x^2 + 13x + 4#


So our final answer is: #(2x^4 - 7x^3 - 2x + 7)/(x^3 + 7x^2 + 13x + 4)#