Algebra

Ch 11 Review

11.4 Simplify

1) 15 – 5x 5x

Do not cancel terms unless they are common factors of the numerator and denominator!!!

=

5x is not a factor of all terms, therefore you cannot cancel 5x!

5(3 – x)

5(x)

= 3 – x x

A common mistake…

2) x2 + 6x + 9 9 – x2

(x + 3)2

=

DTS (3 – x)(3 + x)

x + 3 3 – x

=

5 3

2

7n 10n5n 14n

5

7

8

3

n=

n5=nx

11. 5 Multiplying and Dividing Rational Expressions

2

2

x - 8x +15÷ 3x - 15

x - 3x

1=3x

(x- 5)(x - 3) 1

=x(x - 3) 3(x - 5)

2

2

x - 8x +15 1x - 3x 3x - 15

x x

11.6 Adding/Subtracting Rational Expressions

xx 6

7

3

53

x

x

6

73

53

1)

22

x2

x2

3

2

6

107

x

x

3

2

3

6

7

6

10

x

x

x

2)

x

x

x

x 1

1

2 2

)1(

)1(2 23

xx

xxxx

The LCD is 6x3.

.

.

The LCD is x(x + 1).

(x + 1)(x + 1)

= )1(

12 23

xx

xx

11.7 Dividing Polynomials

9x²

3x

18

3x

12x

3x

Divide 9x² + 12x – 18 by 3x

9x² + 12x – 18

3x= + -

3

1 1

4

1

6

= 3x + 4 - 6x

11.7 Dividing Polynomials

x² - 3x + 5x + 2 Divide x²- 3x + 5 by x + 2

Ask: how many x’s in x²? x

x

Multiply x by x + 2 and subtractx² + 2x

-5x + 5 Ask: how many x’s in -5x? -5

- 5

Multiply -5 by x + 2 and subtract -5x - 10

15 Remainder is 15

Quotient:

Change signs when subtracting!

15x- 5+

x+2

11.8 Solving by cross multiplying.

5y + 2

y

3=1)

5(3) = y(y + 2)

15 = y2 + 2y

-15 -15

0 = y2 + 2y – 15

0 = (y + 5)(y – 3)

y = -5, 3

3x – 7

1

x2 – 9x + 14+ 1 = -2)

+1 +1

Clear the fraction by multiplying each term by the LCD!!

Factor to help find the LCD!!!

(x – 7)(x – 2)

3x – 7

1+ 1 = -

(x – 7)(x – 2)

The LCD is (x – 7)(x – 2)!

(x – 7)(x – 2)(x – 7)(x – 2)

(x – 7)(x – 2)

3x – 6 + x2 – 9x + 14 = -1

x2 – 6x + 8 = -1

x2 – 6x + 9 = 0

(x – 3)2 = 0

x = 3

11.8 Solving by clearing the fractions.

HW

• P. 701-702 #11-28 -Look at your notes/Powerpoints to study -Make-ups today