Examples for

Rational Functions

Rational functions are functions that involve a quotient of polynomial expressions. While rationals share many properties with polynomials, there are some unique aspects that arise due to the division of polynomials, such as asymptotes and singularities. Solve rational equations, find roots, graph, convert to alternate forms, simplify and explore singularities and asymptotes with Wolfram|Alpha.

Rational Functions

Find roots, alternate forms, graphs and other properties of rational functions.

Compute properties of a rational function:

(x^2-1)/(x^2+1)
(t^3+10t^2+32t+32)/(t^2+2t-15)

Find the degree of a rational function:

deg (x^3+x^2-x-1)/(x^3+x^2-2x)

Plot a rational function:

plot (x^5-12x^3+9x)/(x^3-4x)

Simplify a rational expression:

simplify ((x-1)^2(x-2)^3(x^2-1))/(x^3-x^2-4x+4)
(x^4 - 3 x^3 + 5 x^2 - 11 x - 12)/(x - 3) long division

Partial Fractions

Transform rational expressions by decomposing using the partial fractions method.

Compute a partial fraction decomposition:

partial fractions (x^2-4)/(x^4-x)
(x+9)/(x^2-9) in partial fractions

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Step-by-Step Solutions for AlgebraAlgebra Web App

RELATED EXAMPLES

  • Equation Solving
  • Integrals
  • Mathematical Functions
  • Polynomials
  • Simplification