# Simplify Rational Expressions Calculator



A calculator to simplify rational expressions is presented.

## Rational Expressions

Rational expressions are fractions whose numerator and denominator are algebraic expressions. The present calculator add, subtract , multiply, divide and simplify rational expressions .
Example
$\dfrac{x+1}{x+2} - \dfrac{x-1}{(x+2)^2}$ is simplified as follows:
First set both terms to a common denominator $(x+2)^2$
$\dfrac{x+1}{x+2} - \dfrac{x-1}{(x+2)^2} = \dfrac{(x+1)\color{red}{(x+2)}}{(x+2)\color{red}{(x+2)}} - \dfrac{x-1}{(x+2)^2}$
Rewrite the above with the common denominator
$= \dfrac{(x+1)(x+2) - (x-1)}{(x+2)^2}$
Expand terms in the numrator
$= \dfrac{x^2+3x+2 - (x-1)}{(x+2)^2}$
Group like terms
$= \dfrac{x^2+2x+1}{(x+2)^2}$

## Use of the Rational Expressions Calculator

1 - Enter and edit the rational expression and click "Enter Expression" then check what you have entered and edit if needed.
Once the expressions checked, click on "Simplify Expression".

Rational Expression:

Notes: In editing rational expressions, use the following:
1 - The five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: (x+1)/(x-2) + (x+3)*(x+3)/(x+2)^2 )
Here are some examples of rational expressions that you may copy and paste to practice:
2/(x-3) + 5/(x-3)           ( 2/(x-4)) * (5/(x+4))           ( -12/(x+4)) / (12/(x-4))           -3/(x-1) - 5
(2x+2)/(x-1) + (-3x+3)/(x-1)             (4x+2)/(x+2) + (-3x-3)/(x+2) - 2*(x-4)/(x+2) + 2             (-4x+5)/(x-1) + (3x-3)/(x+1)
(x+5)*(x+6)/(2x-1) + (-x-3)/(2x+1)            (-x-5)/(x-1)^2 + (-2x+3)/(x+1)             (-2x+2)/(x-3) + (x+3)/(x-3)^2 - 2*(x-4)/(x-3)
(x+2)/(x-4) + ((x-1)/(x-4))*(3/(x+4))             (2x+1)/(x-5) + ((x-1)/(x-5))/(-6/(x+5))