# Simplify (2x+5)/(x^2-3x)-(3x+5)/(x^3-9x)-(x+1)/(x^2-9)

Simplify each term.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Simplify the denominator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
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 .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Subtract from .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Reorder the factors of .
Combine the numerators over the common denominator.
Simplify the numerator.
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Apply the distributive property.
Multiply by by adding the exponents.
Move .
Multiply by .
Rewrite as .
Subtract from .
Subtract from .
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 (2x+5)/(x^2-3x)-(3x+5)/(x^3-9x)-(x+1)/(x^2-9)