Partial Fractions - Solving Homework Equation with Coefficients

In summary, partial fractions are a method for simplifying equations with coefficients by breaking them down into smaller parts. They are typically used for equations with rational functions and cannot be used for equations with irrational functions. The steps for solving an equation using partial fractions include factoring the denominator, solving for coefficients, and substituting them into the original equation. Common mistakes to avoid include forgetting to factor or incorrectly factoring the denominator and not setting up the correct system of equations. It is important to check the solution by substituting it back into the original equation.
  • #1
cragar
2,552
3

Homework Statement


1/((x^2-1)^2)


Homework Equations





The Attempt at a Solution


so i get (Ax+B)/(x^2-1) + (Cx+D)/((x^2-1)^2)

then i multiply both sides by ((x^2-1)^2)
then i get 1=(Ax+B)(x^2-1)+ (Cx+D)

then i multiply it out Ax^3+Bx^2 -Ax +Cx +D =1
then i equate the coeffcients
A=0 B=0 -A+C=0 -B+D=1 D=1

but when i plug these back in i don't get what my book gets and i setting this up correctly
 
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  • #2
that should be
1/((x^2-1)^2)=A/(x+1)+B/(x+1)^2+C/(x-1)+D/(x-1)^2
 
  • #3
ok i see
 

1. What is the purpose of using partial fractions to solve equations with coefficients?

Partial fractions are used to simplify complex equations with coefficients by breaking them down into smaller, more manageable parts. This makes it easier to solve the equation and find the unknown variables.

2. How do I know when to use partial fractions to solve an equation?

Partial fractions are typically used when an equation contains rational functions, which are fractions where the numerator and denominator are both polynomials. If the degree of the denominator is greater than the degree of the numerator, partial fractions may be necessary to solve the equation.

3. Can I use partial fractions to solve any type of equation?

No, partial fractions are specifically used for solving equations with rational functions. They cannot be used for equations with irrational functions, such as square roots or trigonometric functions.

4. What are the steps for solving an equation using partial fractions?

The first step is to factor the denominator of the rational function into linear or quadratic factors. Then, determine the coefficients of each factor by setting up and solving a system of equations. Finally, substitute the coefficients into the original equation and solve for the unknown variables.

5. Are there any common mistakes to avoid when using partial fractions to solve equations?

One common mistake is forgetting to factor the denominator or incorrectly factoring it. Another mistake is not setting up the correct system of equations to solve for the coefficients. It is also important to check the solution by substituting it back into the original equation to ensure it is correct.

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