Algebra 1 Common Core Student Edition, Grade 8-9

11 - 4 A d d i n g a n d Su b t r ac t i n g Ra t i o n a l Ex p r e ssi o n s

Quick Review Ex e r c i s e s

You can add and subtract rational expressions. To add Add or subtract.
or subtract expressions with like denominators, add or 8x 3
subtract the numerators and write the result over the '• x+ 1 x+ 1
common denominator. To add or subtract expressions with 18. |- + j
different denominators, write the expressions with the LCD 7x 4
and then add or subtract the numerators. 19 5 + x ly- 2 + x x — 4

Ex a m p l e

9 5x

3x - 1 2x + 3

What is a + 7 a — 5 e?

1 a l(a - 5) a{a + 7)

a + 7 a- 5 (a + 7 )(a - 5) (a + 7)(a - 5)

21. Air Travel The distance between Atlanta, Georgia,
    and Albuquerque, New Mexico, is about 1270 mi.
    The groundspeed for jet traffic from Albuquerque
    a — 5 , a + la
    (a + 7)(a - 5) (a + 7)(a - 5) to Atlanta can be about 18% faster than the
    groundspeed from Atlanta to Albuquerque. Let r
    a - 5 + a2 + 7a
    [a + 7)(a - 5)

be the speed from Atlanta to Albuquerque in miles

per hour. What is a simplified expression for the

a2 + 8a — 5

(a + 7)(a - 5)

round-trip flying time?

11 - 5 So l v i n g Ra t i o n a l Eq u a t i o n s

Quick Review

You can solve a rational equation by multiplying each side
by the LCD. Check possible solutions to make sure each
satisfies the original equation.

Ex a m p l e
What is the solution of | + |

3. 4 _ 7

8 x x

to( H )Ml.

3x + 32 = 56

3x = 24

x = 8

Ch eck 3 , 8 8 84 ± 7^

7 7

8 8

Ex e r c i s e s

Solve each equation. Check your solutions.

22 .2 t 81 , 3 = 5

23.

24.

25.

1

m-4 3 [m - 4)

2c „ 4

<o_

m

c — 4

5

2x - 3

c + 5

. 7_
3x
26. Business A new photocopier can make 72 copies in
2 min. When an older photocopier is operational,
the two photocopiers together can make 72 copies
in 1.5 min. How long would it take the older
photocopier to make 72 copies working alone?

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