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Rules of simplifying algebraic fractions

What are the rules for simplifying algebraic fractions?

Simple rules for simplifying algebraic fractions

Rules for simplifying algebraic fractions:

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.

Example of simplifying algebraic fractions

Problem: Simplify the algebraic fractions

32a9 + 36a7
36a7 + 32a7

Solution.

Step by step.

1. Factor the numerator and denominator of the fraction.

The prime factorization of 32

2 * 2 * 2 * 2 * 2 =
25

See 32 prime factorization.

The prime factorization of 36

2 * 2 * 3 * 3 =
22 * 32

See 36 prime factorization.

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

We have

32a9 + 36a7 = 
36a7 + 32a7
25 * a9 + 22 * 32 * a7 = 
22 * 32 * a7 + 25 * a7
(22 * a7)(23 * a2 + 32)
(22 * a7)(32 + 23)

The common factors are 22 and a7.

3. Cancel down all the common factors.

Cancel the common factors

(22a7)(23a2 + 32) = 
(22a7)(32 + 23)
(22a7)(23a2 + 32) = 
(22a7)(32 + 23)
23a2 + 32 = 
32 + 23
8a2 + 9
17

4. The answer is

32a9 + 36a7 = 
36a7 + 32a7
8a2 + 9
17

The problem is solved.