How do you simplify #(x+5)/(x^2+7x+10)#?

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Answer 1 · 2018-07-09T23:14:42

#1/{x+2}#

Given that

#\frac{x+5}{x^2+7x+10}#

#=\frac{x+5}{x^2+5x+2x+10}#

#=\frac{x+5}{x(x+5)+2(x+5)}#

#=\frac{x+5}{(x+5)(x+2)}#

#=1/{x+2}#

Answer 2 · 2018-07-09T23:32:23

#1/(x+2)#

Let's see if we can factor the denominator first. What two numbers sum up to the middle term and have a product of the last term?

After some trial and error, we arrive at #5# and #2#, which means we can factor the denominator as

#(x+5)(x+2)#

We now have the following expression

#(x+5)/((x+2)(x+5))#

Same terms on the top and bottom cancel, and we're left with

#cancel(x+5)/((x+2)cancel(x+5))#

#1/(x+2)#

Hope this helps!