Algebra 1 Common Core Student Edition, Grade 8-9

11-1

Quick Review

A rational expression is an expression that can be written

in the form A rational expression is in simplified

form when the numerator and denominator have no

common factors other than 1.

Ex a m p l e

What is the simplified form o f-

x2 - 9 _ (* + 3)(x - 3)

x2 - 2x - 15 (x + 3)(x - 5)

(xH^3j'(x-3)

x2 - 9

](x- -+ 3)(x

. x — 3
x — 5

5)

• 2x - 15
  Factor the num erator and
  denominator.
  Divide out the common
  factor.

Simplify.

Ex e r c i se s

Simplify each expression. State any excluded values.

4.2x2 + 6x r m —^3

6.

lOx3

x2 + 6x + 9

5x + 15

2s2 - 5s - 12

2s2 - 9s + 4

7.

9.

3 m - 9

2 a2 - 4a + 2

3a2

4 - c

2c- 8

10. Geom et ry What fraction of the
    rectangle is shaded? Write your
    answer as a rational expression
    in simplified form.

11 - 2 an d 11 - 3 Multiplying and Dividing Rat ional Expressions

and Dividing Polynomials

Quick Review

You can multiply and divide rational expressions using the

same properties you use to multiply and divide numerical

fractions.

£ • § = where b d bd’ b + 0 and d ¥= 0.

b d b c be' ~ ~TT> where b + 0, c # 0, and ' ’ d =£ 0.

To divide a polynomial by a monomial, divide each term of

the polynomial by the monomial. To divide a polynomial

by another polynomial, use long division. When dividing

polynomials, write the answer as quotient +

Ex a m p l e

What is the quotient

y , y ~ 3

y + 3 ' y

y y-2

y+3•y-2 y + 3 y — 3

y(y~ 2 )

' (y + 3)(y - 3)

Ex e r c i se s

Multiply or divide.

11 4x + 12 x

12.

13.

x2 - 2 x 6x + 18

a2 + 5a + 4. a2 + 3a + 2

a

x2 + 13x + 40. x + 8

x 2 x2 — 49

14. (12x2 + 9x — 7) -4- 3x


15. {3d2 + 2d- 29) + {d + 3)


16. Geometry The width and area
    of a rectangle are shown in the
    figure at the right. What is the
    length of the rectangle?

(2b - 1) in.

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