# 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

- 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 - Simplify the following algebraic expressions:

(i)

(ii) - 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) x

^{4}-1

(iv) (x +1)(x +2)(x +3)

**2.**(i) 18/7 (ii) 6

**3.**(i) -2/[(x -1)(x -2)(x -3)] (ii) 2 (2x +5)/[ (x +1)(x +2)(x +3)(x +4)]