Simplification of Algebraic Expressions

• Least Common Multiple (L.C.M.) of two or more numbers is the smallest number which can be divided by each of the given numbers. Similar idea applies to algebraic terms or expressions.

• Fractions involving algebraic expressions either in numerator or in denominator (or in both) are called algebraic fractions.Thus x/2, 3/y, (x²-1)/(x²+1) , k/1 etc. are algebraic fractions.

• Such fractions can be reduced to lowest terms by cancelling out common factors in numerator and denominator.

Exercise

1. Find the L.C.M. of(i) 20, 25, 30(ii) a²b, ab, b²(iii) x² -1 and x² +1(iv) x² +3x +2 and x² +5x +6

2. Simplify the following algebraic expressions:(i) (ii) 

3. Simplify the following:(i) [1/(x² -3x +2)] - [1/(x² -5x +6)](ii) [1/(x² +3x + 2)] - [1/(x² +7 x +12)]

Answers

1. (i) 300        (ii) a²b²         (iii) x4 -1    (iv) (x +1)(x +2)(x +3)2. (i) 18/7      (ii) 63. (i) -2/[(x -1)(x -2)(x -3)]         (ii) 2 (2x +5)/[ (x +1)(x +2)(x +3)(x +4)]