Question
What is the product in simplest form? ((x+2)(x-2))/((x+1)(x-1))*((x+1))/(x(x+2))
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Answers
GPT 3.5
To simplify this expression, we can first cancel out common factors in the numerator and denominator:
((x+2)(x-2))/((x+1)(x-1))*(x+1)/(x(x+2))
= (x+2)(x-2)/(x+1)(x-1)*(x+1)/x(x+2)
Now, we can cancel out the common factors in the numerator and denominator:
= (x-2)/(x-1)*1/x
= (x-2)/((x-1)x)
= (x-2)/(x^2-x)
Therefore, the simplified form of the expression is (x-2)/(x^2-x).
((x+2)(x-2))/((x+1)(x-1))*(x+1)/(x(x+2))
= (x+2)(x-2)/(x+1)(x-1)*(x+1)/x(x+2)
Now, we can cancel out the common factors in the numerator and denominator:
= (x-2)/(x-1)*1/x
= (x-2)/((x-1)x)
= (x-2)/(x^2-x)
Therefore, the simplified form of the expression is (x-2)/(x^2-x).