Algebraic Manipulation Worksheets With Answers - Craven Community College Page 10
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2910. The length of a rectangle is 3ft. more than its width. Its area is 28 square ft. Find its dimensions.
11. A room contains 54 chairs. The number of chairs per row is three less than twice the number of rows.
Find the number of rows and the number of chairs per row.
12. A strip of uniform width is to be cut off of both sides and both ends of a sheet of paper that is 8
inches by 11 inches in order to reduce the size of the paper to an area of 40 square inches. Find the width
of the strip.
13. A brace wire is attached to the top of a tower 24m tall. It is anchored 7m from the base of the tower.
How long is the piece of wire between these two points?
14. A ladder is leaning against a wall. The vertical distance up the wall to the top of the ladder is 4ft. less
than the length of the ladder. The distance from the base of the ladder to the wall is 8ft. less than the
length of the ladder. Find the length of the ladder.
R
E
ATIONAL
XPRESSIONS
Multiplying and Dividing Rational Expressions
Rational expressions are fractions where the numerator or the denominator or both are polynomials. The
product of two rational expressions is a rational expression whose numerator is the product of the
numerators and whose denominator is the product of the denominators.
2
2
Example:
X
– 2X
•
2X
– X – 10
2
2
2X
+ X – 15
X
– 4
X(X – 2)
•
(2X – 5)(X + 2)
Factor
(X – 5)(X + 3)
(X – 2)(X + 2)
X(X – 2)(2X – 5)(X + 2)
Multiply
(2X – 5)(X + 3)(X – 2)(X + 2)
X (X – 2)(2X – 5)(X + 2)
Simplify
(2X – 5)(X + 3)(X – 2)(X + 2)
X
Write answer in simplest form
X + 3
The quotient of two rational expressions is the product of the first rational expression and the reciprocal of
the second rational expression.
2
2
Example:
6X
– 7X + 2
÷
4X
– 8X + 3
2
2
3X
+ X – 2
5X
+ X – 4
10
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