# 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".

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))

## More References and Links

Simplify Rational Expressions

Multiply / Divide Rational Expressions

Add / Subtract Rational Expressions