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

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).

Now find the new fractions with the common denominator (5x-2)(x-1).

Now take both numerators and subtract.

-2x+2-(15x-6)= -2x+2-15x+6= -17x+8

The difference in this example is:

Sample Math Problems

Question:

Find the sum. Express the answer as a rational expression.

Answer:

In this problem, the denominators are the same, so we just need to add the numerators.

-2x +10x= 8x

The numerator will be 8x. Since the denominators are the same, we keep a denominator of (x+1)

The sum of this addition problem is 8x/(x+1)

Question:

Find the sum. Express the answer as a rational expression.

Answer:

First find a common denominator. The common denominator will be (x+1)(x-2).

Now find the new fractions with the common denominator (x+1)(x-2).

Now take both numerators and add.

3x-6+x+1=4x-5

The sum will be:

Question:

Find the difference. Express the answer as a rational expression.

Answer:

In this problem, the denominators are the same, so we just need to subtract the numerators.

2x-10x=- 8x