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Rules of simplifying fractions with variables

What are the rules for simplifying fractions with variables?

Simple rules for simplifying fractions with variables

Rules for simplifying fractions with variables:

1. Factor the numerator and denominator of the fraction;
2. Find common factors to both the numerator and denominator;
3. Cancel down all the common factors.

Examples of simplifying fractions with variables

Problem 1: Simplify the fraction with variables

10a
14a2

Solution.

Step by step.

1. Factor the numerator and denominator of the fraction.

The prime factorization of 10

2 * 5

See 10 prime factorization.

The prime factorization of 14

2 * 7

See 14 prime factorization.

2. Find common factors to both the numerator and denominator.

We have

10a = 
14a2
2 * 5 * a
2 * 7 * a2

The common factor is 2a.

3. Cancel down all the common factors.

Cancel the common factor of 2a

2 * 5 * a = 
2 * 7 * a * a
 2a  * 5 = 
 2a  * 7 * a
5
7a

4. The answer is

10a = 5
14a27a

The problem is solved.

Problem 2: Simplify the fraction with variables

4 - a2
2 + a

Solution.

1. Factor the numerator of the fraction.

Factor the numerator

4 - a2 =
22 - a2 =
(2 + a)(2 - a)

2. Find common factors to both the numerator and denominator.

We have

4 - a2 = 
2 + a
(2 + a)(2 - a)
2 + a

The common factor is (2 + a).

3. Cancel down all the common factors.

Cancel the common factor of (2 + a)

(2 + a)(2 - a) = 
2 + a
 (2 + a)  * (2 - a) = 
 2 + a 
2 - a

4. The answer is

4 - a2 = 2 - a
2 + a

The problem is solved.