Algebraic Manipulation Worksheets With Answers - Craven Community College Page 11
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2
6X
– 7X + 2
•
5X
+ X – 4
Write as a multiplication problem
2
2
3X
+ X – 2
4X
– 8X + 3
(2X – 1)(3X – 2)
•
(5X – 4)(X + 1)
Factor, Multiply, and Simplify
(3X – 2)(X + 1)
(2X – 3)(2X – 1)
5X – 4
Write answer in simplest form
2X – 3
Adding and Subtracting Rational Expressions
When adding or subtracting rational expressions with the same denominator, add or subtract the
numerators and keep the common denominator. When adding or subtracting rational expressions with
different denominators, first find the least common denominator for the expressions. Next express each
rational expression in terms of the common denominator. Finally add or subtract the rational expressions
and simplify the result.
Example:
Y + 4
+
Y + l
2
Y
- 5y + 4
Y – 1
Y + 4
+
Y + 1
(Y – 1)(Y + 4)
(Y – 1)
The denominators are factored
The least common denominator is (Y – 1)(Y – 4)
Y + 4
+
(Y + 1)
•
(Y – 4)
Express each using the LCD
(Y – 1)(Y – 4)
(Y – 1)
(Y – 4)
Y + 4 + (Y + 1)(Y – 4)
Add the rational expressions
(Y – 1)(Y – 4)
2
Y + 4 + Y
– 3Y – 4
Simplify
(Y – 1)(Y – 4)
2
Y
– 2Y
(Y – 1)(Y – 4)
Y(Y – 2)
There are no common factors.
(Y – 1)(Y – 4)
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