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!

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