simplify((1+x)^3/(1+x))

The original denominators must be nonzero: x ≠ -1
Let's reduce: (1 + x)31 + x
The fraction: (1 + x)31 + x simplifies by the common factor: 1 + x into the new expression: (1 + x)2
▶Simplified form:   (x + 1)2

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