How do you multiply #((x+1)^2) / (x-1) * [(2x-2)/ (x+1)]#?

1 Answer
Mr. Mike
Apr 17, 2018

#((x+1)^2)/(x-1)*((2x-2)/(x+1))=2x+2#

Explanation:

Simplify FIRST! This makes you life much easier! Notice that the #x+1# factor in the denominator of the second quotient CANCELS OUT one of the #x+1# factors in the numerator of the first quotient.

#((x+1)^cancel(2))/(x-1)*((2x-2)/cancel(x+1))=((2x-2)(x+1))/(x-1)#

Now note that we can factor a 2 out of the second factor in the numerator.

#=((2x-2)(x+1))/(x-1)=(2(x-1)(x+1))/(x-1)#

Now cancel the #x-1# factor.

#(2cancel((x-1))(x+1))/cancel(x-1)=2(x+1)=2x+2#

Note that for this example, there was very little multiplication required to multiply these quotients. Mostly we divided.

Related questions
See all questions in Multiplication of Rational Expressions
Impact of this question
1784 views around the world
You can reuse this answer
Creative Commons License