Question

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

Answer 1

`((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.