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Example 2. Solve :(y 1 )(y 2 ) (y 4 )(y 2 )

Solution :(y 1 )(y 2 ) (y 4 )(y 2 )

or, y^2 y 2 y 2 y^2  4 y 2 y 8

or, y 2 2 y 8

or, y 2 y  8  2 [by transposition]

or, y  6

or, y 6

? Solution is y 6

Example 3. Solve and write the solution set :
5

2 1

7 1

2 4

15

6 1 







 x

x

x x

Solution :
5

2 1

7 1

2 4

15

6 1 







 x

x

x x

or,
7 1

2 4

5

2 1

15

6 1











x

x x x

[by transposition]

or,
7 1

2 4

15

6 1 6 3



   

x

x x x or,

7 1

2 4

15

4





x

x

or, 15 ( 2 x 4 ) 4 ( 7 x 1 ) [by cross-multiplication]

or, 30 x 60 28 x 4
or, 30 x 28 x 60  4 [by transposition]
or, 2 x 56 , or x 28
? Solution is x 28
and solution set is S { 28 }.

Example 4. Solve :
5

1

2

1

4

1

3

1











x x x x

Solution :
5

1

2

1

4

1

3

1 `











x x x x

or,
( 2 )( 5 )

5 2

( 3 )( 4 )

4 3

 

  

 

  

x x

x x

x x

x x

or,

7 10

2 7

7 12

2 7

(^22)  

 

x x
x
x x
x
Values of the fractions of two sides are equal. Again, numerators of two sides are
equal, but denominators are unequal. In this case, if only the value of the numerators
is zero, two sides will be equal.
? 2 x 7 0 or, 2 x 7
or,
2
7
x
? Solution is
2
x 7