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Created on: 2011-12-25

A sample problem solved by Quickmath online algebra solver

Command

Partial Fractions

Expression
(x^3+x^2+1)/(x*(x-1)*(x^2+x+1)*(x^2+1)^3)

  1. A fraction: the top of the fraction is a sum that contains 3 terms; the 1st term of the sum is a power; the base is x; the exponent is three; the 2nd term of the sum is a power; the base is x; the exponent is two; the 3rd term of the sum is one; the bottom of the fraction is a product that comprises 4 factors; the 1st factor of the product is equal to x; the 2nd factor of the product is a sum containing 2 terms; the 1st term of the sum is x; the 2nd term of the sum is equal to negative one; the 3rd factor of the product is equal to a sum containing 3 terms; the 1st term of the sum is equal to a power; the base is x; the exponent is two; the 2nd term of the sum is equal to x; the 3rd term of the sum is one; the 4th factor of the product is a power; the base is a sum containing 2 terms; the 1st term of the sum is a power; the base is x; the exponent is two; the 2nd term of the sum is one; the exponent is three;
  2. x to the power of three plus x raised to the power of two plus one fraction line x multiplied by opening brace x plus negative one closing brace multiplied by open bracket x raised to the power two plus x plus one close bracket multiplied by left bracket x exponentiated by two plus one right bracket exponentiated by three.
Result
(-x-1)/(x^2+x+1)+(15*x-1)/(8*(x^2+1))+(3*x+3)/(4*(x^2+1)^2)-(x-1)/(2*(x^2+1)^3)-1/x+1/(8*(x-1))

  1. A sum that comprises 6 terms; the 1st term of the sum is equal to a rational expression: the numerator of the rational expression is a sum that contains 2 terms; the 1st term of the sum is negative x; the 2nd term of the sum is negative one; the denominator of the rational expression is a sum comprising 3 terms; the 1st term of the sum is equal to a power; the base is x; the exponent is two; the 2nd term of the sum is x; the 3rd term of the sum is equal to one; the 2nd term of the sum is equal to a rational expression: the top of the rational expression is a sum that comprises 2 terms; the 1st term of the sum is equal to a product that comprises 2 factors; the 1st factor of the product is equal to fifteen; the 2nd factor of the product is equal to x; the 2nd term of the sum is equal to negative one; the bottom of the rational expression is a product of 2 factors; the 1st factor of the product is equal to eight; the 2nd factor of the product is a sum containing 2 terms; the 1st term of the sum is equal to a power; the base is x; the exponent is two; the 2nd term of the sum is one; the 3rd term of the sum is a fraction: the numerator of the fraction is a sum consisting of 2 terms; the 1st term of the sum is a product of 2 factors; the 1st factor of the product is equal to three; the 2nd factor of the product is x; the 2nd term of the sum is equal to three; the denominator of the fraction is a product that contains 2 factors; the 1st factor of the product is four; the 2nd factor of the product is equal to a power; the base is a sum containing 2 terms; the 1st term of the sum is equal to a power; the base is x; the exponent is two; the 2nd term of the sum is equal to one; the exponent is two; the 4th term of the sum is a negative fraction: the top of the fraction is a sum containing 2 terms; the 1st term of the sum is equal to x; the 2nd term of the sum is negative one; the bottom of the fraction is a product comprising 2 factors; the 1st factor of the product is two; the 2nd factor of the product is equal to a power; the base is a sum that comprises 2 terms; the 1st term of the sum is a power; the base is x; the exponent is two; the 2nd term of the sum is one; the exponent is three; the 5th term of the sum is equal to a negative fraction: the numerator of the fraction is one; the denominator of the fraction is x; the 6th term of the sum is equal to a fraction: the top of the fraction is one; the bottom of the fraction is a product containing 2 factors; the 1st factor of the product is equal to eight; the 2nd factor of the product is equal to a sum of 2 terms; the 1st term of the sum is equal to x; the 2nd term of the sum is equal to negative one;
  2. negative x plus negative one fraction line x exponentiated by two plus x plus one plus fifteen multiplied by x plus negative one over eight times left brace x to the power of two plus one right brace plus three multiplied by x plus three fraction line four multiplied by open bracket x to the power of two plus one close bracket exponentiated by two plus negative x plus negative one over two times opening brace x exponentiated by two plus one closing brace raised to the power three plus negative one divided by x plus one over eight times open bracket x plus negative one close bracket.