Title

1 9

14 14h The easiest way to solve a

fraction equation is to first get rid of the fraction !!!

Multiply each term by the common denominator!!

(14) (14) (14)

This will cancel the denominator, leaving just numerators!!

1 9

h has a denominator of one, so just multiply 14 times h.

14h 1 114h 814 14

h 8

144

7h

Ex. 1

3 1

8 8m

First, multiply each term by the common denominator!!

(8) (8) (8)

This will cancel the denominator, leaving just numerators!!3 1m has a denominator of one, so just multiply 8 times m.

8m 3 38m 28 8m 2

8

1

4m

Ex. 2

52 8

9y

Even though the problem looks different, follow the same steps.

First, multiply each term by the common denominator!!

(9) (9) (9)

-2 and 8 have a denominator of one, so just multiply (-2)(9) and (8)(9).

5y 18 72 18 18

5y 905 5y 18

Ex. 3

32 4

5x First, multiply each term by

the common denominator!!

(5) (5) (5)

-2 and 4 have a denominator of one, so just multiply (-2)(5) and (4)(5).

3x 10 20 10 10

3x 303 3

x 10

Ex. 4

The problem looks different again but still follow the same steps.

First, multiply each term by the common denominator!! What is it?

1 5 2

12 12 3x

(12) (12) (12)

x 5NOW, divide 3 into 12. This will cancel the 3.

This will give you 4. Now multiply 4(-2).

4

815 5

x 3

Ex. 5

1 5 1

3 12 2x

First, multiply each term by

the common denominator!! What is it?

(12) (12) (12)

5

4

3 will go into 12, 4 times. (4)(-1) =4x 2 will go into 12, 6 times. (6)(1) =

6

65 5

4x 114 4x 11

4

or324

x

Ex. 6

• Separate the double fraction then use same steps as before!!

• The x – 8 becomes x + -8 when we separate the fractions.

Now multiply by LCD. Fix your signs back. Now solve for “x”

816

7

x

167

x

8

7

( 7) ( 7) ( 7)

112 x 8

112 8x 88

x104

Ex. 7

3 ( 4)9

6

n

• Separate the

double fraction AND fix your double sign.3

6

n

Ex. 8

4

6

9

( 6) ( 6) ( 6)

3n 4 544 4

3n 503 3

50

3n 2

163

nor

5( 1)75 11

x x

Ex. 9 • With this type of problem you will FIRST distribute, THEN separate.

• Get rid of the LCD. What is it?

• 5(11) = 555

11

x 5

117

5

x

(55) (55)(55) (55)

385

11

11x

5

25x

5

2525x25x

385 36x 25385 385

36x 360

36 360x 36 36

10x

2( 6)116 32

x x

Ex. 10

2

32

x 12

321

16

x

(32) (32)(32) (32)2

32 2x 2x 122x2x

32 4x 1232 32

4x 20

4 20x 4 4

5x

USE THESE STEPS• First Distribute• Separate• Multiply by LCD• Solve

3 1 35

4 4

xx

Ex. 11

USE THESE STEPS• Separate• Multiply by LCD• Solve3 1 3

54 4 4

xx

(4) (4) (4) (4)

3x 1 3x 203x3x201

What happened to the variables?

The variables cancelled each other out. The statement left says 1 = 20. IS THAT TRUE OR FALSE?

If the statement had been TRUE, the answer would have been ALL REAL NUMBERS