How To Add & Subtract Radical Expressions With Fractions

Adding and subtracting radical expressions with fractions is exactly the same as adding and subtracting radical expressions without fractions, but with the addition of rationalizing the denominator to remove the radical from it. This is done by multiplying the expression by the value 1 in an appropriate form.

Step 1

Write down the radical expression.

Step 2

Simplify the first term. (The square root of 9 is 3.)

Step 3

Rationalize the first term. Multiply the term by a fraction equivalent to 1 using the radical as both the numerator and denominator.

Step 4

Simplify the rationalized first term. (The square root of 25 is 5.)

Step 5

Simplify the second term. (Write the term over 1.)

Step 6

Rationalize the second term. Multiply the term by a fraction equivalent to 1. If possible, use a number that will give us a denominator common to that of the first term in Step 4. (Which is 5 here.)

Step 7

Simplify the rationalized second term. (It is not possible here.)

Step 8

Write down the complete expression with the answers from Step 4 and Step 7.

Step 9

Merge the numerator over the common denominator, if one exists. (5 here.)

Step 10

Complete the order of operations to get the answer.

Step 11

Simplify the answer, if possible. (It is not possible here.)

Step 12

Write down the radical expression.

Step 13

Repeat Steps 2 through Step 7 from Section 1 above.

Step 14

Write down the complete expression.

Step 15

Merge the numerator over the common denominator, if one exists. (5 here.)

Step 16

Complete the order of operations to get the answer.

Step 17

Simplify the answer, if possible. (It is not possible here.)