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Created on: 2011-12-24

A sample problem solved by Quickmath online algebra calculator

creating partial fractions from 9*x/y-y/x/(3/y-1/x)

Command

Partial Fractions

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

  1. A fraction: the numerator of the fraction is a power. The base is x. The exponent is two. The denominator of the fraction is a product that consists of 2 factors. The first factor of the product is a sum comprising 2 terms. The first term of the sum is negative x. The second term of the sum is one. The second factor of the product is equal to a power. The base is a sum containing 2 terms. The first term of the sum is a power. The base is x. The exponent is two. The second term of the sum is one. The exponent is two.
  2. x to the power two fraction line left brace negative x plus one right brace multiplied by left bracket x raised to the power of two plus one right bracket raised to the power of two.
Result
(x+1)/(4*(x^2+1))-(x+1)/(2*(x^2+1)^2)-1/(4*(x-1))

  1. A sum that contains 3 terms. The first term of the sum is equal to a quotient: dividend of the quotient is a sum that contains 2 terms. The first term of the sum is equal to x. The second term of the sum is equal to one. Divisor of the quotient is a product that consists of 2 factors. The first factor of the product is four. The second factor of the product is equal to a sum comprising 2 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 one. The second term of the sum is a negative fraction: the numerator of the fraction is a sum consisting of 2 terms. The first term of the sum is equal to x. The second term of the sum is equal to one. The denominator of the fraction is a product that contains 2 factors. The first factor of the product is equal to two. The second factor of the product is a power. The base is a sum comprising 2 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 one. The exponent is two. The third term of the sum is a negative quotient: dividend of the quotient is one. Divisor of the quotient is a product comprising 2 factors. The first factor of the product is equal to four. The second factor of the product is equal to a sum that contains 2 terms. The first term of the sum is equal to x. The second term of the sum is equal to negative one.
  2. x plus one divided by four times opening parenthesis x raised to the power two plus one closing parenthesis plus negative x plus one fraction line two times left brace x exponentiated by two plus one right brace to the power two plus negative one over four times opening brace x plus negative one closing brace.