do now: pass out calculators. work on eoc review week # 21. have your agenda out with your...

Do Now:

• Pass out calculators. • Work on EOC Review Week # 21. • Have your agenda out with your

assignments written down for a scholar dollar and your current grade.

Objective:

• To Simplify Rational Expressions.

Lesson 12.4 Simplify Rational

Expressions Rational Expression - Can be written as a fraction but the denominator cannot be 0.

*A rational expression is undefined when the denominator is 0.

Excluded Value – A number that makes a rational expression undefined.

EXAMPLE 1 Find excluded values

Find the excluded values, if any, of the expression.

a. x + 810x

SOLUTION

a. The expression x + 8 is undefined when 10x = 0, or x = 0. 10x

ANSWER

The excluded value is 0.



b. 2y + 14

5

SOLUTION

The expression 5 is undefined when

2y + 14 = 0, or x = – 7.2y + 14

ANSWER

The excluded value is – 7.



c. v 2 – 9

4v

SOLUTION

c. The expression 4v is undefined when v2 – 9 = 0,

or (v + 3)(v – 3) = 0. The solutions of the equation are

– 3 and 3.

v2 – 9

The excluded values are – 3 and 3.

ANSWER



d. 7w + 28w 2 + w + 5

SOLUTION

d. The expression 7w + 28w 2 + w + 5

is undefined when

8w2 + w + 5 = 0.

The discriminant is b2 – 4ac = 12 – 4(8)(5) < 0. So, the quadratic equation has no real roots.

ANSWER

There are no excluded values.

GUIDED PRACTICE for Example 1


x + 23x – 5

1.

ANSWER

The excluded value is .53

2.2

5y2 + 2y +3

ANSWER

There are no excluded values.



3. n – 6

2n2 – 5n – 12

ANSWER

The excluded value is and 4 .32

–

4. 2mm2 – 4

ANSWER

The excluded value is 2, and 2 .–

EXAMPLE 2 Simplify expressions by dividing out monomials

Simplify the rational expression, if possible. State the excluded values.

a. r2r

SOLUTION

Divide out common factor.a. r2r = r

2r

=12 Simplify.

ANSWER


EXAMPLE 2


b. 5x5(x + 2)

SOLUTION

b. 5x5(x + 2)

= 5 x5 (x + 2) Divide out common factor.

Simplify.= x(x + 2)

ANSWER


Simplify expressions by dividing out monomials

EXAMPLE 2


SOLUTION

c. 6m3 – 12m3

18m2

c.18m2

6m3 – 12m3 =

6m2 (m – 2)6 3 m2

Factor numerator and denominator.

=6m2 (m – 2)6 3 m2 Divide out common factors.

= m – 2 3

Simplify.

ANSWER



EXAMPLE 2


SOLUTION

d. y7 – y

d. The expression y

7 – yis already in simplest form.

ANSWER




5. 4 a3

22a6

211a3

ANSWER The excluded value is 0.

6.2c

c + 5 2c

c + 5ANSWER The excluded value is – 5.

7. 2s2 + 8s3s +12

ANSWER 2s3


8.8x

8x3 + 16x2ANSWER

1

x2 + 2xThe excluded values are 0 and – 2.

EXAMPLE 3 Simplify an expression by dividing out binomials

Simplify x2 – 3x – 10x2 + 6x + 8

. State the excluded values.

SOLUTION

x2 – 3x – 10x2 + 6x + 8

=(x – 5)(x + 2)(x + 4)(x + 2)


(x – 5)(x + 2)(x + 4)(x + 2)

=

= x – 5x + 4

Divide out common factor.

Simplify.

ANSWER

The excluded values are – 4 and – 2.

EXAMPLE 4 Recognize opposites

Simplify x2 – 7x + 1216 – x2

. State the excluded values.

SOLUTION

x2 – 7x + 12 16 – x2


(x – 3)(x – 4)– (x – 4)(4 + x)

= Rewrite 4 – x as – ( x – 4).

Simplify.

– (x – 4)(4+ x)(x – 3)(x – 4)

= Divide out common factor.

–(4 + x)(x – 3)

=

(x – 3)(x – 4) (x – 4)(4 + x)=

ANSWER

The excluded values are – 4 and 4.

(x + 4)(x – 3)

= –

GUIDED PRACTICE for Examples 3 and 4

Simplify the rational expression. State the excluded values.

9. x2 + 3x + 2

x2 + 7x + 10

(x + 1)

(x + 5)ANSWER The excluded values

are – 2 and – 5.

10.y2 – 64

y2 – 16y + 64 ANSWER

(y + 8)

(y – 8)

The excluded value is 8

11.5 + 4z – z2

z2 – 3z – 10ANSWER

(z + 1)

(z + 2)

– The excluded values are 5 and – 2.

do now: pass out calculators. work on eoc review week # 21. have your agenda out with your...

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