How do you simplify #\frac { x ^ { 2} - 2x - 15} { x ^ { 2} - 9} \cdot \frac { x + 3} { x - 5}#?

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Answer 1 · 2016-10-20T21:18:42

#(x+3)/(x-3)#

#\frac { x ^ { 2} - 2x - 15} { x ^ { 2} - 9} \cdot \frac { x + 3} { x - 5}#

Factor the fraction on the left

What are the factors of -15 that add up to -2

#(x-5)(x+3)#

Difference of perfect squares

#(x^2-9)=(x^2-3^2)=(x+3)(x-3)#

Rewrite the expression using the factors you just found

#((x-5)(x+3))/((x+3)(x-3))*(x+3)/(x-5)#

Now cross cancel

#(cancel(x-5)cancel(x+3))/(cancel(x+3)(x-3))*(x+3)/cancel(x-5)#

You are then left with

#(x+3)/(x-3)#

Answer 2 · 2016-10-20T21:21:03

The expression can be simplified to #(x + 3)/(x- 3)#.

#=((x - 5)(x + 3))/((x + 3)(x- 3)) xx (x + 3)/(x - 5)#

#=(x + 3)/(x - 3)#

Hopefully this helps!