How do you multiply and simplify #\frac { x ^ { 2} + 5x - 14} { x ^ { 2} + 6x - 16} \cdot \frac { 2x + 16} { x + 6}#?

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Answer 1 · 2017-08-21T15:49:41

#(2x+14)/(x+6)#

Factor numerators and denominators to get

# ((x+7)(x-2))/((x+8)(x-2)) xx (2(x+8))/(x+6).#

Cancel like factors to get"

# ((x +7) xx2)/(x+6) #

#= (2x+14)/(x+6)#

Answer 2 · 2017-08-21T16:00:04

#(2x+14)/(x+6)#

First, let's factor everything that can be factored. I'm going to look at each set of terms individually. Note that #x+6# cannot be factored.

#x^2+5x-14=(x+7)(x-2)#

#x^2+6x-16=(x+8)(x-2)#

#2x+16=2(x+8)#

Now that we have the factored terms, let's put these factors into the expression.

#((x+7)(x-2))/((x+8)(x-2))*(2(x+8))/(x+6)#

Now that we have the factored terms, we see that the numerator and denominator have #x-2# and #x+8# in common. These terms will cancel out.

#((x+7)(x-2))/((x+8)(x-2))*(2(x+8))/(x+6) ->#

#((x+7)(cancel(x-2)))/((cancel(x+8))(cancel(x-2)))*(2(cancel(x+8)))/(x+6) ->#

When you cancel the terms out, you get the following.

#(2(x+7))/(x+6)=(2x+14)/(x+6)#