How do you simplify #(x+5)/(x-3)*(7x^2 - 21x) / (7x)#?

1 Answer
Rafael · Stefan V.
Sep 21, 2015

#x+5#

Explanation:

Completely factor out all expressions. You can factor out 7x from #(7x^2-21x)#.

#(x+5)/(x-3)*(7x^2-21x)/(7x)#

#=(x+5)/(x-3)*[(7x)(x-3)]/(7x)#

#=[(x+5)(7x)(x-3)]/[(7x)(x-3)]#

After you have factored everything out, cancel factors that appear in both the numerator and the denominator. In this problem, #7x# and #(x-3)# appear in both the numerator and denominator, so you can cancel them.

#[(x+5)cancel((7x))cancel((x-3))]/[cancel((7x))cancel((x-3))]#

#=(x+5)/1#

#=x+5#

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