Factor using the AC method.

Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .

Write the factored form using these integers.

Simplify the denominator.

Rewrite as .

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

To write as a fraction with a common denominator, multiply by .

To write as a fraction with a common denominator, multiply by .

Multiply and .

Multiply and .

Reorder the factors of .

Reorder the factors of .

Combine the numerators over the common denominator.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Apply the distributive property.

Multiply by .

Apply the distributive property.

Multiply by .

Subtract from .

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Move to the left of .

Simplify (5r)/(r^2+2r-35)-r/(r^2-49)