# 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 63 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 153 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 xx 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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