# Split Using Partial Fraction Decomposition (13x+11)/(x^4-1)

Decompose the fraction and multiply through by the common denominator.
Factor the fraction.
Rewrite as .
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify.
Rewrite as .
Factor.
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
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 is 2nd order, terms are required in the numerator. The number of terms required in the numerator is always equal to the order of the factor in the denominator.
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.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify each term.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Multiply by .
Multiply by .
Expand by multiplying each term in the first expression by each term in the second expression.
Combine the opposite terms in .
Reorder the factors in the terms and .
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Move to the left of .
Rewrite as .
Multiply by by adding the exponents.
Move .
Multiply by .
Move to the left of .
Rewrite as .
Multiply by by adding the exponents.
Move .
Multiply by .
Move to the left of .
Rewrite as .
Combine the opposite terms in .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Apply the distributive property.
Multiply by .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Move to the left of .
Rewrite as .
Move to the left of .
Rewrite as .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Apply the distributive property.
Multiply by .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Multiply by .
Multiply by .
Simplify the expression.
Move .
Reorder and .
Reorder and .
Move .
Reorder and .
Reorder and .
Reorder and .
Reorder and .
Move .
Move .
Move .
Move .
Move .
Move .
Create equations for the partial fraction variables and use them to set up a system of equations.
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 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 the system of equations.
Simplify each equation.
Rewrite as .
Rewrite as .
Simplify each term.
Rewrite as .
Rewrite as .
Solve for in the first 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 both sides of the equation.
Replace all occurrences of in with .
Simplify .
Simplify each term.
Apply the distributive property.
Multiply .
Multiply by .
Multiply by .
Multiply .
Multiply by .
Multiply by .
Solve for in the third equation.
Rewrite the equation as .
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify each equation.
Simplify .
Simplify each term.
Apply the distributive property.
Multiply .
Multiply by .
Multiply by .
Combine the opposite terms in .
Subtract from .
Simplify .
Simplify each term.
Apply the distributive property.
Multiply .
Multiply by .
Multiply by .
Simplify .
Simplify each term.
Apply the distributive property.
Multiply .
Multiply by .
Multiply by .
Solve for in the second equation.
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Subtract from both sides of the equation.
Replace all occurrences of in with .
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Simplify terms.
Combine fractions with similar denominators.
Simplify the expression.
Subtract from .
Divide by .
Solve for in the fourth equation.
Rewrite the equation as .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
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.
Simplify .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Simplify .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Replace each of the partial fraction coefficients in with the values found for , , , and .
Simplify each term.
Combine and .
Move to the left of .
Split Using Partial Fraction Decomposition (13x+11)/(x^4-1)
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