Simplifying Polynomial Fractions Worksheet
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1
2
3Lesson 13
CA Standard Alg 1 12.0
Simplifying Polynomial
Fractions
Fractions with polynomials in the numerator and/or denominator can often
be simplified by factoring and reducing to lowest terms. For example, the
x
2
2 4x 2 21
fraction
can be simplified to x + 3 by factoring the numerator
x 2 7
2
x
1 x 2 12
and reducing to lowest terms. Likewise, the fraction
can be
2
x
2 x 2 20
x 2 3
simplified to
by factoring both the numerator and the denominator
x 2 5
and reducing to lowest terms.
Polynomials in the Numerator or the Denominator
To simplify a fraction with a factorable polynomial in the numerator or the
denominator, first factor the polynomial in the numerator or the
denominator. Then reduce the fraction to lowest terms by canceling out any
monomials or polynomials that exist in both the numerator and denominator,
if possible. Finally, recombine terms by multiplying any monomials or
polynomials that remain in the numerator or denominator.
EXAMPLE 1
2x 2 9
Simplify the fraction
2
2x
y 2 xy 2 36y
Step 1 Factor completely the polynomial in the denominator.
2x 2 9
2x 2 9
2x 2 9
5
5
2
2
y(2x 2 9)(x 1 4)
2x
y 2 xy 2 36y
y(2x
2 x 2 36)
Step 2 Reduce the fraction to lowest terms by canceling out any monomials or
polynomials that exist in both the numerator and denominator.
2x 2 9
2x 2 9
1
5
5
y(2x 2 9)(x 1 4)
y(2x 2 9)(x 1 4)
y(x 1 4)
Step 3 Use Distributive Property to rewrite the denominator.
1
1
5
xy 1 4y
y(x 1 4)
CA Standards Check 1
2
y 2 32y
4z 1 1
8x
1a. Simplify the fraction
.
1b. Simplify the fraction
.
x 1 2
2
4z
2 27z 2 7
37
CA Standards Review
LESSON 13
■
Simplifying Polynomial Fractions
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