How do you simplify #\frac { x ^ { 2} + 5x + 4} { 2x ^ { 2} + 4x - 16} \div \frac { x ^ { 2} - x - 2} { 3x ^ { 2} - x - 2}#?

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Answer 1 · 2016-12-06T17:05:26

#((3x + 2)(x - 1))/((2x - 4)(x - 2))#

First, factor each quadratic equation:

#((x + 4)(x + 1))/((2x - 4)(x + 4)) -: ((x - 2)(x + 1))/((3x + 2)(x - 1))#

Then we can rewrite this as:

#(((x + 4)(x + 1))/((2x - 4)(x + 4)))/(((x - 2)(x + 1))/((3x + 2)(x - 1)))#

Using the rules for dividing fractions gives us:

#((x + 4)(x + 1)(3x + 2)(x - 1))/((2x - 4)(x + 4)(x - 2)(x + 1))#

#(cancel((x + 4))cancel((x + 1))(3x + 2)(x - 1))/((2x - 4)cancel((x + 4))(x - 2)cancel((x + 1)))#

#((3x + 2)(x - 1))/((2x - 4)(x - 2))#