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Created on: 2012-04-10

A sample problem solved by Quickmath math solver

splitting a sum that comprises 4 terms. x/(x+1)*(x+2)^2 to partial fractions | making partial fractions from 4*s^2+8*s+10

Command

Simplify

Expression
(1/s^2+1)^4/(16*(1/s-s)^3)+(1/(s^6*(1/s-s)^2)-(1/s^2+1)^2/(2*s^3*(1/s-s)^2))

  1. A sum of 2 terms. The 1st term of the sum is equal to a fraction: the numerator of the fraction is a power. The base is a sum that contains 2 terms. The 1st term of the sum is equal to a quotient: dividend of the quotient is one. Divisor of the quotient is a power. The base is s. The exponent is two. The 2nd term of the sum is equal to one. The exponent is four. The denominator of the fraction is a product of 2 factors. The 1st factor of the product is sixteen. The 2nd factor of the product is equal to a power. The base is a sum consisting of 2 terms. The 1st term of the sum is equal to a rational expression: the numerator of the rational expression is one. The denominator of the rational expression is s. The 2nd term of the sum is equal to negative s. The exponent is three. The 2nd term of the sum is equal to a sum that consists of 2 terms. The 1st term of the sum is a rational expression: the top of the rational expression is one. The bottom of the rational expression is a product consisting of 2 factors. The 1st factor of the product is equal to a power. The base is s. The exponent is six. The 2nd factor of the product is equal to a power. The base is a sum that consists of 2 terms. The 1st term of the sum is equal to a rational expression: the top of the rational expression is one. The bottom of the rational expression is s. The 2nd term of the sum is equal to negative s. The exponent is two. The 2nd term of the sum is a negative quotient: dividend of the quotient is a power. The base is a sum containing 2 terms. The 1st term of the sum is a quotient: dividend of the quotient is one. Divisor of the quotient is a power. The base is s. The exponent is two. The 2nd term of the sum is one. The exponent is two. Divisor of the quotient is a product comprising 3 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 s. The exponent is three. The 3rd factor of the product is a power. The base is a sum that consists of 2 terms. The 1st term of the sum is a rational expression: the top of the rational expression is one. The bottom of the rational expression is s. The 2nd term of the sum is equal to negative s. The exponent is two.
  2. opening parenthesis one over s exponentiated by two plus one closing parenthesis exponentiated by four over sixteen times opening bracket one over s plus negative s closing bracket to the power three plus left brace one fraction line s raised to the power six multiplied by left bracket one fraction line s plus negative s right bracket to the power two plus negative open brace one divided by s raised to the power of two plus one close brace to the power two divided by two times s raised to the power of three multiplied by left brace one fraction line s plus negative s right brace exponentiated by two right brace.
Result
-(s^8+12*s^6+14*s^4-16*s^3-4*s^2+16*s-7)/(16*s^11-48*s^9+48*s^7-16*s^5)

  1. A rational expression: the top of the rational expression is a negative sum comprising 7 terms. The 1st term of the sum is equal to a power. The base is s. The exponent is eight. The 2nd term of the sum is a product that consists of 2 factors. The 1st factor of the product is equal to twelve. The 2nd factor of the product is equal to a power. The base is s. The exponent is six. The 3rd term of the sum is equal to a product that consists of 2 factors. The 1st factor of the product is equal to fourteen. The 2nd factor of the product is a power. The base is s. The exponent is four. The 4th term of the sum is equal to a negative product of 2 factors. The 1st factor of the product is sixteen. The 2nd factor of the product is equal to a power. The base is s. The exponent is three. The 5th term of the sum is equal to a negative product that consists of 2 factors. The 1st factor of the product is equal to four. The 2nd factor of the product is a power. The base is s. The exponent is two. The 6th term of the sum is equal to a product containing 2 factors. The 1st factor of the product is equal to sixteen. The 2nd factor of the product is equal to s. The 7th term of the sum is negative seven. The bottom of the rational expression is a sum that comprises 4 terms. The 1st term of the sum is a product that consists of 2 factors. The 1st factor of the product is equal to sixteen. The 2nd factor of the product is a power. The base is s. The exponent is eleven. The 2nd term of the sum is equal to a negative product comprising 2 factors. The 1st factor of the product is equal to forty eight. The 2nd factor of the product is equal to a power. The base is s. The exponent is nine. The 3rd term of the sum is equal to a product consisting of 2 factors. The 1st factor of the product is forty eight. The 2nd factor of the product is equal to a power. The base is s. The exponent is seven. The 4th term of the sum is equal to a negative product that comprises 2 factors. The 1st factor of the product is sixteen. The 2nd factor of the product is equal to a power. The base is s. The exponent is five.
  2. negative left bracket s exponentiated by eight plus twelve multiplied by s raised to the power six plus fourteen multiplied by s raised to the power of four plus negative sixteen multiplied by s raised to the power of three plus negative four multiplied by s to the power of two plus sixteen times s plus negative seven right bracket fraction line sixteen times s to the power eleven plus negative forty eight times s raised to the power of nine plus forty eight times s exponentiated by seven plus negative sixteen times s raised to the power of five.