To divide by a fraction, multiply by its reciprocal.

Factor by grouping.

For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .

Reorder terms.

Reorder and .

Factor out of .

Rewrite as plus

Apply the distributive property.

Move parentheses.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, .

Rewrite as .

Factor out of .

Factor out of .

Factor out of .

Move a negative from the denominator of to the numerator.

Reorder terms.

Combine the numerators over the common denominator.

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

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor.

Rewrite the expression.

Cancel the common factor.

Divide by .

Multiply by .

Divide ((a^2)/(2a-b)+(b^2)/(b-2a))÷(((a+b)^2)/(2a^2+ab-b^2))