Factor ((p^2-q^2)/(p+q))÷((p+q)/(p-q))

p2-q2p+q÷p+qp-q

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=p and b=q.

(p+q)(p-q)p+qp+qp-q

Reduce the expression by cancelling the common factors.

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Reduce the expression (p+q)(p-q)p+q by cancelling the common factors.

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Cancel the common factor.

(p+q)(p-q)p+qp+qp-q

Rewrite the expression.

p-q1p+qp-q

Divide p-q by 1.

p-qp+qp-q

Factor ((p^2-q^2)/(p+q))÷((p+q)/(p-q))

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