Regents Exam Questions A.A.16: Rational Expressions 1 Name:
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1
A.A.16: Rational Expressions 1: Simplify fractions with polynomials in the numerator and
denominator by factoring both and renaming them to lowest terms
1 The expression 9x 4 27x
6
3x 3 is equivalent to
1) 3x(1 3x)
2) 3x(1 3x 2
)
3) 3x(1 9x 5
)
4) 9x
3
(1 x)
2 Which expression represents 2x 2 12x
x 6 in simplest
form?
1) 0
2) 2x
3) 4x
4) 2x 2
3 Which expression is in simplest form?
1) x
x 2
2) 9
x 2 9
3) x 2 4
x 2
4) x 2 6x 9
x 2 x 6
4 Which expression represents x 2 2x 15
x 2 3x
in
simplest form?
1) 5
2) x 5
x
3) 2x 5
x
4) 2x 15
3x
5 For all values of x for which the expression is
defined, 2x x 2
x 2 5x 6 is equivalent to
1) 1
x 3
2) x
x 3
3) 1
x 2
4) x
x 2
6 Which expression represents 25x 125
x 2 25 in simplest
form?
1) 5
x
2) 5
x
3) 25
x 5
4) 25
x 5
Regents Exam Questions A.A.16: Rational Expressions 1 Name:
www.jmap.org
2
7 Which expression represents x 2 x 6
x 2 5x 6
in
simplest form?
1) x 2
x 2
2) x 6
5x 6
3) 1
5
4) 1
8 Express x 2 3x 10
x 2 5x
as a fraction in simplest form.
9 Express in simplest form: x 2 5x 24
x 2 8x
10 Simplify: x 2 6x 5
x 2 25
11 Simplify:
9x 2 15xy
9x 2 25y 2
12 The area of a rectangle is represented by
x 2 5x 24. If the width of the rectangle is
represented by x 8, express the length of the
rectangle as a binomial.
ID: A
1
A.A.16: Rational Expressions 1: Simplify fractions with polynomials in the numerator and
denominator by factoring both and renaming them to lowest terms
Answer Section
1 ANS: 2
9x 4 27x
6
3x 3 9x 4
(1 3x 2
)
3x 3 3x(1 3x 2
)
REF: fall0718ia
2 ANS: 2
2x 2 12x
x 6 2x(x 6)
x 6 2x
REF: 060824ia
3 ANS: 2
. .
REF: 060712b
4 ANS: 2
x 2 2x 15
x 2 3x (x 5)(x 3)
x(x 3) x 5
x
REF: 060921ia
5 ANS: 2
REF: 060202b
6 ANS: 4
25x 125
x 2 25 25(x 5)
(x 5)(x 5) 25
x 5
REF: 080821ia
7 ANS: 1
x 2 x 6
x 2 5x 6 (x 3)(x 2)
(x 3)(x 2) x 2
x 2
REF: 011130ia
8 ANS:
x 2
x
REF: 088704siii
ID: A
2
9 ANS:
x 3
x . x 2 5x 24
x 2 8x (x 8)(x 3)
x(x 8) x 3
x
REF: 060837a
10 ANS:
x 1
x 5 .
REF: 010631a
11 ANS:
3x
3x 5y
REF: 069924a
12 ANS:
x 2 5x 24
x 8 (x 8)(x 3)
x 8 x 3
REF: 061131ia
Step-by-step explanation:
To write a rational expression in lowest terms, we must first find all common factors (constants, variables, or polynomials) or the numerator and the denominator. Thus, we must factor the numerator and the denominator. Once the numerator and the denominator have been factored, cross out any common factors.
