Simplify ((x+4)/(x-1))/((x^2+x)/(x-1))

Problem

(x+4)/(x−1)/(x2+x)/(x−1)

Solution

1. Rewrite the complex fraction as a multiplication problem by multiplying the numerator by the reciprocal of the denominator.

(x+4)/(x−1)⋅(x−1)/(x2+x)

2. Factor the denominator of the second fraction by taking out the greatest common factor, which is x

(x+4)/(x−1)⋅(x−1)/(x*(x+1))

3. Cancel the common factor (x−1) from the numerator and the denominator.

(x+4)/1⋅1/(x*(x+1))

4. Multiply the remaining numerators and denominators to find the simplified expression.

(x+4)/(x*(x+1))

Final Answer

(x+4)/(x−1)/(x2+x)/(x−1)=(x+4)/(x*(x+1))

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