Rewrite the division as a fraction.

Multiply the numerator by the reciprocal of the denominator.

Rewrite as .

Check the middle term by multiplying and compare this result with the middle term in the original expression.

Simplify.

Factor using the perfect square trinomial rule , where and .

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Factor out of .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply and .

Move to the left of .

Reorder factors in .

Divide ((x^2+2x+1)/(x^2-1))÷(2x^2+2x)