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

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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)#.