How do you divide and simplify #\frac { x ^ { 2} + 9x - 22} { x ^ { 2} + 12x + 11} \div \frac { 2x ^ { 2} - 4x - 6} { 3x ^ { 2} - 3}#?

1 Answer
graces
May 6, 2017

First, you have to multiply by the reciprocal.

Explanation:

Remember that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal means that the numerator and denominator are flipped.

So it becomes:
#[(x^2+9x-22)/(x^2+12x+11)]*[(3x^2-3)/(2x^2-4x-6)]#

Then you have to F.O.I.L. for the numerator and denominator.
After you combine like terms, you end up with:
#(3x^4+27x^3-69x^2-27x-66)/(2x^4+20x^3-32x^2-116)#

Next notice how a 3 can be factored out of the numerator, and a 2 can be factored out of the denominator.
Like this:
#(3(x^4+9x^3-23x^2-9x-22))/(2(x^4+10x^3-16x^2-58))#
This is the simplest form.

Hope this helps :)

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