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11.5. Simplify Rational Expressions. Rational Expression: a fraction whose numerators and denominators are polynomials. Examples: 3 , 2x , and 6 . x + 4 x 2 – 9 x 2 + 1.

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simplify rational expressions

11.5

Simplify Rational Expressions

slide2

Rational Expression: a fraction whose numerators and denominators are polynomials.

Examples: 3 , 2x , and 6 . x + 4 x2 – 9 x2 + 1

slide3

Domain: the set of all real numbers except those for which the denominator is zero.

For example: The domain of 3 is x + 4 all real numbers except -4.

slide4

Simplify Rational Expression the same way that you reduce a fraction.

Divide the numerator and denominator by “x”

25

=

Divide the numerator and denominator by “2”

2x + 4

=

slide5

Domain:x can be any real number except a number that would make the denominator 0!

Find the domain of each expression below.

slide6

How do you know when your rational expression is reduced?

Reduced Form: when the numerator and denominators have no common factors except for ±1.

the rule
The RULE:

To simplify fractions, divide out common factors.

REMEMBER you can’t cancel out +(adding) and –(subtracting)

slide8

For a,b,c any non-zero real numbers,

Remember you can only cancel out FACTORS!!!

slide9

Simplify the expression.

x2 + 4x +4

Factor each polynomial.

x2 - 4

(x + 2)(x + 2)(x + 2)(x – 2)

What does the numerator and denominator have in common?

Factor out (x + 2)

The answer is: x + 2 x - 2

simplify the expression
Simplify the expression.

Factor each polynomial.

x2 - 7x + 12x2 +3x - 18

(x - 4)(x – 3)(x + 6)(x - 3)

What does the numerator and denominator have in common?

Factor out (x – 3)

The answer is: x - 4 x + 6