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.

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