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

Question

Kennedy Adams · Accepted Answer

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

Kennedy Adams · Answer

undefined To simplify the expression ((x+1)^2) / (x-1) * [(2x-2)/ (x+1)], we can follow these steps:

Step 1: Simplify the numerator of the first fraction, ((x+1)^2), by expanding it:
((x+1)^2) = (x+1)(x+1) = x^2 + 2x + 1

Step 2: Simplify the denominator of the first fraction, (x-1).

Step 3: Simplify the numerator of the second fraction, (2x-2), by factoring out the common factor of 2:
(2x-2) = 2(x-1)

Step 4: Simplify the denominator of the second fraction, (x+1).

Step 5: Combine the simplified fractions by multiplying the numerators and denominators together:
[(x^2 + 2x + 1) / (x-1)] * [2(x-1) / (x+1)]

Step 6: Simplify the expression further by canceling out common factors between the numerators and denominators:
[(x^2 + 2x + 1) * 2] / (x+1)

Step 7: Multiply the terms in the numerator:
(2x^2 + 4x + 2) / (x+1)

Therefore, the simplified expression is (2x^2 + 4x + 2) / (x+1).

Eva Adamson · Answer

undefined To simplify $\frac{(x+1)^2}{x-1} \times \frac{2x-2}{x+1}$, first factor the expressions and cancel out common factors. After canceling common factors, simplify the expression further. The simplified expression is $2(x + 1)$.