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Algebraic Equations with Fractions

Rules for solving Algebraic Equations with Fractions

1) Find the common denominator (LCM).
2) Multiply the whole Algebra Equation by LCM.
3) Solve it as a normal equation.

Example 1:
x 5
--- - --- = 6
3 2

LCM of 3 and 2 = 6
Multiply both side by 6
x 5
[--- - --- = 6 ] x 6
3 2
2x - 15 = 36
+ 15 = + 15
------------------
2x 51
---- = ------
2 2
x = 51 / 2

Check : For x = 51 / 2 ;
Left side = 51 / ( 2 x 3) - 5 / 2
= 17 / 2 - 5 /2 = 12 / 2 = 6
= Right side
Example 2:
x x
--- + --- = 8
3 5

LCM of 3 and 5 = 15
Multiply both side by 15
x 5
[--- + --- = 8 ] x 15
3 5
5x + 3x = 120
8x = 120
8x 120
---- = ----
8 8
x = 15

Check : For x = 15;
Left side = 15 / 3 + 15 / 5
= 5 + 3 = 8
= Right side
1 2
--- + --- = 3
x x

LCM = x
Multiply both side by x
1 2
[--- + --- = 3 ] X x
x x
1 + 2 = 3x
3 = 3x ⇒ x = 1

Check : For x = 1 ;
Left side = 1 / 1 + 2 / 1
= 1 + 2 = 3
= Right side

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