Factor out of .

Factor out of .

Factor out of .

Factor out of .

For each factor in the denominator, create a new fraction using the factor as the denominator, and an unknown value as the numerator. Since the factor in the denominator is linear, put a single variable in its place .

For each factor in the denominator, create a new fraction using the factor as the denominator, and an unknown value as the numerator. Since the factor in the denominator is linear, put a single variable in its place .

For each factor in the denominator, create a new fraction using the factor as the denominator, and an unknown value as the numerator. Since the factor in the denominator is linear, put a single variable in its place .

Multiply each fraction in the equation by the denominator of the original expression. In this case, the denominator is .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Apply the distributive property.

Multiply by .

Simplify each term.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Apply the distributive property.

Move to the left of .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Multiply by .

Cancel the common factor.

Rewrite the expression.

Divide by .

Apply the distributive property.

Move to the left of .

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 .

Move to the left of .

Multiply by .

Subtract from .

Multiply by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Rewrite as .

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 .

Move to the left of .

Multiply by .

Subtract from .

Apply the distributive property.

Simplify.

Rewrite using the commutative property of multiplication.

Move to the left of .

Simplify the expression.

Reorder and .

Reorder and .

Move .

Move .

Move .

Move .

Move .

Create an equation for the partial fraction variables by equating the coefficients of from each side of the equation. For the equation to be equal, the equivalent coefficients on each side of the equation must be equal.

Create an equation for the partial fraction variables by equating the coefficients of from each side of the equation. For the equation to be equal, the equivalent coefficients on each side of the equation must be equal.

Create an equation for the partial fraction variables by equating the coefficients of the terms not containing . For the equation to be equal, the equivalent coefficients on each side of the equation must be equal.

Set up the system of equations to find the coefficients of the partial fractions.

Solve for in the first equation.

Rewrite the equation as .

Subtract from both sides of the equation.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Replace all occurrences of in with .

Simplify each equation.

Remove parentheses.

Subtract from .

Simplify .

Multiply by .

Add and .

Solve for in the second equation.

Rewrite the equation as .

Add to both sides of the equation.

Replace all occurrences of in with .

Simplify .

Simplify each term.

Apply the distributive property.

Multiply by .

Multiply by .

Add and .

Solve for in the third equation.

Rewrite the equation as .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Replace all occurrences of in with .

Simplify.

Multiply by .

Simplify .

Multiply by .

Add and .

Replace each of the partial fraction coefficients in with the values found for , , and .

Split Using Partial Fraction Decomposition (2x+172)/((x-4)^2(x+5))