How to Simplify Complex Fractions Easily! (2 Methods)

Описание: Learn two powerful methods to simplify complex fractions in this algebra tutorial! Mario's Math Tutoring demonstrates how to eliminate fractions within fractions.

Method 1: Combine and Divide First, combine the fractions in the numerator into a single fraction and do the same for the denominator. Then, treat the main fraction bar as division and multiply by the reciprocal ("keep it, change it, flip it").

Method 2: Clear Denominators (Least Common Multiple) Identify the least common multiple (LCM) of all denominators within the complex fraction. Multiply the entire numerator and the entire denominator of the complex fraction by this LCM to clear all inner denominators simultaneously.

We'll work through two examples, applying both methods so you can choose your favorite!

In this video, you'll discover:

0:00 Introduction to Simplifying Complex Fractions
0:30 What is a Complex Fraction?
0:50 Method 1: Combine and Divide
1:10 Example 1: (3/(x-2) - 2/(x+2)) / (4/(x²-4) + x/(x+2))
1:20 Getting Common Denominators in the Numerator
2:30 Combining Numerator Fractions (Remember Parentheses for Subtraction!)
3:40 Factoring Denominators for Common Denominators
4:30 Combining Denominator Fractions
5:10 "Keep it, Change it, Flip it" (Multiply by Reciprocal)
6:00 Canceling Common Factors and Final Simplified Answer
6:50 Method 2: Clear Denominators (Least Common Multiple)
7:20 Finding the LCM of All Denominators
8:30 Multiplying Numerator and Denominator by the LCM
9:10 Distributing the LCM and Clearing Denominators
10:30 Simplifying and Combining Like Terms
11:10 Comparing Results from Method 1 and Method 2
12:00 Example 2: (5/(x-1)) / (2/(x+3) + 3/x)
12:20 Method 1: Combining Denominator Fractions
13:00 Factoring Denominators and Getting Common Denominators
14:30 Combining Denominator Fractions and Distributing
15:30 "Keep it, Change it, Flip it" and Canceling Factors
16:30 Final Simplified Answer for Method 1
17:00 Method 2: Clearing Denominators with LCM
17:20 Finding the LCM of All Denominators
18:10 Distributing the LCM and Clearing Denominators
19:10 Simplifying and Combining Like Terms
20:00 Final Simplified Answer for Method 2
Master complex fractions and simplify with confidence using these powerful techniques!

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