This document discusses rational expressions and how to simplify them. It explains that to simplify a rational expression, you factor the numerator and denominator and divide out common factors. Examples are provided to demonstrate this process. Exercises are included for the reader to practice simplifying rational expressions.

1. RATIONAL EXPRESSIONS
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2. Rational Expression
Objective
To be able to simplify a rational expression
PRIME! numerator
5
x + 2
denominator
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3. Rational Expressions
Simplifying rational expressions
- Factor the numerator.
- Factor the denominator.
- Divide out the common factors.
- Write in simplified form.
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4. Rational Expressions
Simplifying rational expressions
2
3x + 9x Step 1: Look for common factors
3 to both terms in the numerator.
12x
- 3 is a factor of both 3 and 9.
- x is a factor of both x2 and x.
Step 2: Factor the numerator
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5. Rational Expressions
Simplifying rational expressions
2
3x + 9x Step 3: Look for common factors in
the denominator
3
12x There’s only one term in the
denominator but it can still be
factored out.
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6. Rational Expressions
Simplifying rational expressions
2
3x + 9x
3 Step 4: Divide and simplify
12x
x +3
2
4x
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7. Rational Expressions
Exercises
2
9 x yz
1. 2
24 xyz
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8. Rational Expressions
Exercises
9 x yz 2 3x
1. 2
=
24 xyz 8z
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9. Rational Expressions
Exercises
a + 3
2. 2
a + 4a + 3
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10. Rational Expressions
Exercises
a + 3 1
2. 2
+ 4a + 3
=
a a +1
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11. Rational Expressions
Exercises
3x − 15
3. 2
x − 7x + 10
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12. Rational Expressions
Exercises
3x − 15 3
3. 2
− 7x + 10
=
x x − 2
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