Adding And Subtracting Rational Expressions

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Adding And Subtracting Rational Expressions | Algebra Math Help

What is a rational expression?

A rational expression is a fraction made up of polynomials. Both the numerator and the denominator will be a polynomial.

How to add and subtract rational expressions?

Adding Rational Expressions With Like Denominators:

When adding rational expressions with like denominators, add the numerators and keep the denominator the same.

In the example below, both expressions have the same denominator of x.

To add these, add the numerators 2 and -5 to get a sum of -3. Then keep the denominator x. This gives you an answer of

\frac{-3}{x}

Adding Rational Expressions With Unlike Denominators:

When adding rational expressions with unlike denominators, first find a common denominator. In the example below, the common denominator will be (x-1)(1-x).

Now find the new fractions with the common denominator (x-1)(1-x)

Now take both numerators and add.

x-x²+ x-1= -x²+2x-1

The new rational expression will be:

The answer to this example is 1.

Subtracting Rational Expressions With Like Denominators:

When subtracting rational expressions with like denominators, subtract the numerators and keep the denominator the same.

In this example both expressions have the same denominator of 3x.

To subtract these, subtract -2 from 1. 1-(-2) =3. Then keep the denominator 3x.This gives you an answer of 3/3x. When simplified, the difference will be 1/x.

Subtracting Rational Expressions With Unlike Denominators:

When subtracting rational expressions with unlike denominators, first find a common denominator. In the example below, the common denominator will be (5x-2)(x-1).