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Created on: 2012-01-05

A sample problem solved by Quickmath web algebra calculator

partial fraction decomposition of a sum of 2 terms. (x^4+9*x+15)/((x-1)*(x^2+4)^2) | splitting a sum comprising 4 terms. to partial fractions

Command

Partial Fractions

Expression
(7*x^2+x+4)/(6*x*(x^2-3*x+4))

  1. A fraction: the top of the fraction is a sum that consists of 3 terms; the first term of the sum is a product that comprises 2 factors; the first factor of the product is seven; the second factor of the product is equal to a power; the base is x; the exponent is two; the second term of the sum is x; the third term of the sum is four; the bottom of the fraction is a product that comprises 3 factors; the first factor of the product is equal to six; the second factor of the product is x; the third factor of the product is equal to a sum comprising 3 terms; the first term of the sum is equal to a power; the base is x; the exponent is two; the second term of the sum is a negative product comprising 2 factors; the first factor of the product is equal to three; the second factor of the product is equal to x; the third term of the sum is equal to four;
  2. seven times x to the power two plus x plus four over six multiplied by x multiplied by open brace x raised to the power of two plus negative three multiplied by x plus four close brace.
Result
(3*x+2)/(3*(x^2-3*x+4))+1/(6*x)

  1. A sum that comprises 2 terms. The first term of the sum is a rational expression: the top of the rational expression is a sum of 2 terms. The first term of the sum is equal to a product of 2 factors. The first factor of the product is three. The second factor of the product is equal to x. The second term of the sum is equal to two. The bottom of the rational expression is a product comprising 2 factors. The first factor of the product is three. The second factor of the product is equal to a sum comprising 3 terms. The first term of the sum is equal to a power. The base is x. The exponent is two. The second term of the sum is equal to a negative product containing 2 factors. The first factor of the product is equal to three. The second factor of the product is equal to x. The third term of the sum is equal to four. The second 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 first factor of the product is six. The second factor of the product is equal to x.
  2. three times x plus two over three times opening brace x to the power two plus negative three times x plus four closing brace plus one divided by six multiplied by x;