Add and subtract rational expressions

Key Notes :

To add rational expressions with common denominators, add the numerators.

Learn with an example

Simplify. Express your answer as a single fraction in simplest form.

5/2q4+4/5 __________

Before you can add, the expressions must have a common denominator.

The lowest common multiple (LCM) of 2q4 and 5 is 10q4 . Rewrite each expression with a denominator of 10q4 .

5/2q4+4/5

5/2q4 . 5/5 + 4/5 .2q4 /2q4

25/10q4 + 8q4/10q4

Now that the expressions have a common denominator, you can add the numerators.

8q4+25/10q4

Simplify. Express your answer as a single fraction in simplest form.

4/r5-5/r __________

Before you can subtract, the expressions must have a common denominator.

The lowest common multiple (LCM) of  r5 and r is r5 . Rewrite the second expression with a denominator of r5.

4/r5-5/r

4/r5-5/r . r4/r4

4/r5 – 5r4/r5

Now that the expressions have a common denominator, you can subtract the numerators.

-5r4+4/r5

Simplify. Express your answer as a single fraction in simplest form.

3/8yz + 5z/2 __________

Before you can add, the expressions must have a common denominator.

The lowest common multiple (LCM) of 8yz  and 2 is 8yz   . Rewrite the second expression with a denominator of 8yz

3/8yz + 5z/2

3/8yz + 5z/2 . 4yz/4yz

3/8yz + 20yz2/8yz

Now that the expressions have a common denominator, you can add the numerators.

3 + 20yz2/8yz

let’s practice!