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Created on: 2012-01-21

A sample problem solved by Quickmath online math solver

Command

Partial Fractions

Expression
(t^2+t^4)/(1-2*t^2+t^4+(-2)*t^6)

  1. A fraction: the numerator of the fraction is a sum of 2 terms. The 1st term of the sum is equal to a power. The base is t. The exponent is two. The 2nd term of the sum is a power. The base is t. The exponent is four. The denominator of the fraction is a sum consisting of 4 terms. The 1st term of the sum is equal to one. The 2nd term of the sum is equal to a negative product that comprises 2 factors. The 1st factor of the product is equal to two. The 2nd factor of the product is equal to a power. The base is t. The exponent is two. The 3rd term of the sum is equal to a power. The base is t. The exponent is four. The 4th term of the sum is equal to a product comprising 2 factors. The 1st factor of the product is negative two. The 2nd factor of the product is equal to a power. The base is t. The exponent is six.
  2. t raised to the power of two plus t raised to the power four divided by one plus negative two times t to the power of two plus t to the power four plus left parenthesis negative two right parenthesis times t to the power six.
Result
-(t^2+3)/(5*(t^4+1))-3/(5*(2*t^2-1))

  1. A sum comprising 2 terms; the 1st term of the sum is a rational expression: the top of the rational expression is a negative sum comprising 2 terms; the 1st term of the sum is equal to a power; the base is t; the exponent is two; the 2nd term of the sum is three; the bottom of the rational expression is a product of 2 factors; the 1st factor of the product is equal to five; the 2nd factor of the product is a sum of 2 terms; the 1st term of the sum is equal to a power; the base is t; the exponent is four; the 2nd term of the sum is equal to one; the 2nd term of the sum is a negative quotient: dividend of the quotient is three; divisor of the quotient is a product comprising 2 factors; the 1st factor of the product is five; the 2nd factor of the product is a sum containing 2 terms; the 1st term of the sum is equal to a product comprising 2 factors; the 1st factor of the product is equal to two; the 2nd factor of the product is a power; the base is t; the exponent is two; the 2nd term of the sum is equal to negative one;
  2. negative open bracket t to the power of two plus three close bracket divided by five times open bracket t exponentiated by four plus one close bracket plus negative three over five times opening parenthesis two multiplied by t raised to the power two plus negative one closing parenthesis;