How do you simplify $(5x) /( x+2) * (x^2 +7x +10 )/(25x^2)$ ?

Question

2252 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-19T20:18:39

$(x+5)/(5x)$

First, you must factor the trynomial

$x^2+7x+10=(x+2)(x+5)$

so

$(5x)/(x+2)*(x^2+7x+10)/(25x^2)$

$(color(red)5cancelx)/cancel(x+2)*(cancel(x+2)(x+5))/(color(red)25x^cancel2)$

$(x+5)/(5x)$

Answer 2 · 2016-06-19T20:21:17

It is $(x+5)/(5x)$ .

We can start simplifying the $5x$ and $25x^2$

$(5x)/(x+2)*(x^2+7x+10)/(25x^2)$

$=(cancel(5x))/(x+2)*(x^2+7x+10)/(cancel(5x)*5x)$

$=(x^2+7x+10)/(5x(x+2))$

the next step is to factorize $x^2+7x+10$

$x^2+7x+10=(x+5)(x+2)$

then

$(x^2+7x+10)/(5x(x+2))$

$((x+5)cancel((x+2)))/(5xcancel((x+2)))$

$=(x+5)/(5x)$ .

How do you simplify (5x) /( x+2) * (x^2 +7x +10 )/(25x^2)(5x) /( x+2) * (x^2 +7x +10 )/(25x^2)?