Algebra 1 Common Core Student Edition, Grade 8-9

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Problem 4

What is the difference

Subtracting Expressions W ith Different Denominators

3 2 o

d - 1

St e p 1 Find th e LCD of

St e p 2

d + 2'

and •^2

d - l d + 2-

Since there are no com m on factors, the LCD is (d — 1 ){d + 2).

Rewrite each rational expression using the LCD an d th e n subtract.

3 2 3 (d + 2 ) 2(d — 1)

Should you multiply
the denominator or
leave it in factored
form?
There might be common
factors to divide out later.
So leave the denominator
in factored form.

d - 1 d + 2 [ d - 1 ){d + 2) (d - l) ( d + 2)

3d + 6 _____________2d-2

(d - 1 )(d + 2 ) (d - l)(d + 2 )

3d + 6 - {2 d - 2)

(d - 1 )(d + 2 )

d+ 8

{d - 1 )(d + 2 )

G o t It? 4. W hat is th e d iffe re n c e : c 4

Rewrite each fraction using the LCD.

Simplify each numerator.

Subtract the numerators.

Simplify the numerator.

3c - l c - 2 •

'y j Problem 5 Using Rational Expressions

Gas Mileage A certain truck gets 25% better gas mileage when it holds no cargo than

when it is fully loaded. Let m be the number of miles per gallon of gasoline the truck

gets when it is fully loaded. The truck drops off a full load and returns empty. What is

an expression for the number of gallons of gasoline the truck uses?

How can unit anal ysi s

help you?

You can use unit analysis

to verify that gallons of

gasoline used equals

distance traveled divided

by miles per gallon.

mi _ 9al _ „ , i

mi/gal ’ ml 3a

St e p 1

St e p 2

return trip

Write expressions for th e a m o u n t of gasoline

used on the outw ard trip a n d on the re tu rn trip.

rv O utw ard trip: gasoline u sed = —, d is ta n c e tra v e le d r.-----------ti— = 80

r ° miles per gallon 171

tR e t u r n t r ip : g a s o l i n e u s e d = m ile s p e r g a llo n,. ,. j distance traveled 80

Add th e expressions to find th e total am o u n t

of gasoline the truck uses.

total gasoline u sed = j ^ + \

80(1.25) 80

T25W + L 2 5 m Rewrlte USln3 th e LCD' 1 ■2 5 m■

1.25m 1.25m Simplify the first numerator.

180

1.25m Add the numerators.

TTT Si mpl i f y.

6 8 6 C h a p t e r 11 Rat io nal Expressions and Funct ions