Simplify ((x+1)^3(x-2)+3(x+1)^2)/((x+1)^4)

Problem

((x+1)3*(x−2)+3*(x+1)2)/((x+1)4)

Solution

1. Identify the common factor in the terms of the numerator. Both terms contain (x+1)2

2. Factor out the greatest common factor (x+1)2 from the numerator.

(x+1)2*[(x+1)*(x−2)+3]

3. Expand the expression inside the brackets.

(x+1)*(x−2)+3=x2−2*x+x−2+3

x2−x+1

4. Rewrite the entire fraction with the factored numerator.

((x+1)2*(x2−x+1))/((x+1)4)

5. Simplify the fraction by canceling (x+1)2 from the numerator and the denominator.

(x2−x+1)/((x+1)2)

Final Answer

((x+1)3*(x−2)+3*(x+1)2)/((x+1)4)=(x2−x+1)/((x+1)2)

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