This document explains the addition and subtraction of algebraic fractions and how to solve fractional equations. It details the process of finding the lowest common denominator (lcd) and clearing fractions from equations by multiplying through by the lcd. The document also contains examples and homework exercises for practice.

1. Ch9
9.4: Addition and Subtraction of algebraic Fraction
9.5: Solving Fractional Equation
Week 10
Monday 11/11/2019

2. Addition and Subtraction of algebraic Fraction
• Now that you know how to find the LCD, you can add and subtract
Algebraic fraction with different denominators
Example: 1. Factor completely.
2. Determine the LCD.
3. For each term, multiply the
numerator and denominator by any
factors that are in the LCD, but not in
that denominator.
4. Perform the addition/subtraction
and simplify the numerator

3. Example:

4. Practice:

5. Solving Fractional Equation
• A fractional equation is one that contains fraction terms.
• TO SOLVE AN EQUATION WITH fractions, we transform it into an equation without fractions (which
we know how to solve). The technique is called clearing of fractions.
Example: Solve for x, =6
1st
. Multiply both sides of the equation -- every term -- by the LCD of denominators. We have two
denominator
3,5 , so find
LCD for both
3, 5
LCD of 3, 5 is 15, So we multiply both sides of the equation by 15
15.
𝑥
3
+15.
(𝑥− 2)
5
=15.6
Now we have the following simple equation that has been "cleared" of fractions:
5 𝑥+3(𝑥−2)=90
2nd
. solve the equation.

6. 3rd
. Check your answer for restriction ( because sometimes the solution has correct procedure to find x, BUT the
value of x dose not satisfy the equation (if we substitute the x value the statement will be false) .

7. Example:

8. Example:
• when a single fraction is equal to a single fraction, then the equation can be cleared by "cross-
multiplying."

9. Practice: Solve for x,

10. Homework
• P(318): 9.4 # 1,3,5,7,8,9,11,13,15
• P (326): 9.5 # 1,2,3,4,5, 7, 17, 19, 21,23