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Created on: 2012-03-03

A sample problem solved by Quickmath online math calculator

Command

Partial Fractions

Expression
1/((1-0.3*x^-1)*(1-0.4*x^-1)*(1-x^-1)*(1-x^-1))

  1. A rational expression: the top of the rational expression is one; the bottom of the rational expression is a product that consists of 4 factors; the 1st factor of the product is a sum of 2 terms; the 1st term of the sum is equal to one; the 2nd term of the sum is equal to a negative product that contains 2 factors; the 1st factor of the product is equal to zero point and three tenth; the 2nd factor of the product is equal to a power; the base is x; the exponent is negative one; the 2nd factor of the product is equal to a sum consisting of 2 terms; the 1st term of the sum is equal to one; the 2nd term of the sum is equal to a negative product that consists of 2 factors; the 1st factor of the product is equal to zero point four; the 2nd factor of the product is a power; the base is x; the exponent is negative one; the 3rd factor of the product is equal to a sum consisting of 2 terms; the 1st term of the sum is one; the 2nd term of the sum is a negative power; the base is x; the exponent is negative one; the 4th factor of the product is equal to a sum that contains 2 terms; the 1st term of the sum is one; the 2nd term of the sum is a negative power; the base is x; the exponent is negative one;
  2. one fraction line open bracket one plus negative zero point and three tenth multiplied by x to the power negative one close bracket times opening bracket one plus negative zero point and four tenth multiplied by x exponentiated by negative one closing bracket times left brace one plus negative x to the power of negative one right brace times left brace one plus negative x to the power negative one right brace.
Result
-81/(49*(10*x-3))+32/(9*(5*x-2))+950/(441*(x-1))+50/(21*(x-1)^2)+1

  1. A sum of 5 terms. The 1st term of the sum is a fraction: the top of the fraction is negative eighty one. The bottom of the fraction is a product of 2 factors. The 1st factor of the product is forty nine. The 2nd factor of the product is a sum of 2 terms. The 1st term of the sum is equal to a product containing 2 factors. The 1st factor of the product is ten. The 2nd factor of the product is equal to x. The 2nd term of the sum is equal to negative three. The 2nd term of the sum is equal to a fraction: the top of the fraction is thirty two. The bottom of the fraction is a product that consists of 2 factors. The 1st factor of the product is equal to nine. The 2nd factor of the product is equal to a sum comprising 2 terms. The 1st term of the sum is a product that consists of 2 factors. The 1st factor of the product is five. The 2nd factor of the product is x. The 2nd term of the sum is negative two. The 3rd term of the sum is equal to a rational expression: the numerator of the rational expression is nine hundred and fifty. The denominator of the rational expression is a product consisting of 2 factors. The 1st factor of the product is four hundred and forty one. 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 negative one. The 4th term of the sum is equal to a quotient: dividend of the quotient is fifty. Divisor of the quotient is a product that contains 2 factors. The 1st factor of the product is equal to twenty one. The 2nd factor of the product is equal to a power. The base is a sum comprising 2 terms. The 1st term of the sum is equal to x. The 2nd term of the sum is negative one. The exponent is two. The 5th term of the sum is equal to one.
  2. negative eighty one fraction line forty nine times left parenthesis ten times x plus negative three right parenthesis plus thirty two fraction line nine multiplied by opening brace five times x plus negative two closing brace plus nine hundred and fifty fraction line four hundred and forty one times open parenthesis x plus negative one close parenthesis plus fifty over twenty one times opening bracket x plus negative one closing bracket exponentiated by two plus one.