• NOTES 11.5

ADD AND SUBTRACTRATIONAL EXPRESSIONS

IDENTIFY VARIABLE RESTRICTIONS

Add: 2

31

yx

Get common denominators and rename numerators

x

x

yy

y

x 22

2 31

Multiply numerators and combine like terms.

2

2 3

xy

xy

LCD = xy2

Add:3

3

9

22

xx

Factor the denominator if possible

3

3

)3)(3(

2

xxx

)3(

)3(

3

3

)3)(3(

2

x

x

xxx

)3)(3(

73

xx

x

Add:xx

x 6

1

4

Factor the denominator if possible

1

16

1

4

x

x

xx

x

x

x

Multiply numerators and combine like terms.

)1(

664 2

xx

xx

Simplify:

11

1

y

yx

x

xyx

xy

2

xy

xy

Simplify Complex Fractions

)1)(1

)()(1

xyxyy

xyyx

xyx

FORMULAS FOR NEXT SLIDE:

Combined mpg =

gal

mimpg

mpg

migal

galgal

milesmiles

A WOMAN DRIVES AN SUV THAT GETS 10MPG. HER HUSBAND DRIVES A HYBRID THAT GETS 60MPG. EVERY WEEK, THEY

TRAVEL THE SAME NUMBER OF MILES. THEY WANT TO IMPROVE THEIR COMBINED MPG AND HAVE 2 OPTIONS.

Option 1: Tune the SUV and increase its mileage by 1mpg and keep the hybrid as it is.Option 2: Buy a new hybrid that gets 80mpg and keep the SUV as it is.

mpg8.17mpg6.18

xx

x

1160

)660)(2(

6011xxxx

Option 1 Option 2

Tuned SUV: 11mpg, Hybrid: 60mpg

SUV: 10mpg, New Hybrid: 80mpggalhybridgalSUV

mihybridmiSUVmpgcombined

660

660

8010xxxx

80

80

xx

x

8

)80)(2(

HW: P489-490, # 13-22, 27, 29, 30B, 31-35