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