If p(x)/q(x) and r(x)/s(x) are 2 rational expressions then their difference is given by

when q(x)≠s(x)

and if q(x)=s(x) then

Example 1

Find the difference of 2x+5/x and x+3/2x

2x+5/x- x+3/2x

In the denominators, the irreducible factors are 2,x

The highest exponents of these factors are 1,1

∴ LCM = 2, x

Example 2

Find the value of

Irreducible factors are a, b, c.

The highest exponents are 2, 2, 2

LCM = a²b²c²

Comparing with

Example 3

Find the value of

This is the of the form p(x)/q(x)-r(x)/s(x)

Comparing with

Example 4

Find the value of

Factorizing only the denominators we get

The irreducible factors in the denominator are x+1, x-3, x2+3x+9

The highest exponents of these factors are 1, 1, 1

∴ LCM= (x+1) ( x-3) (x2 + 3x + 9)

Then

Try these questions

Find the values of:

1. 

2. 

3. 

4. 

5. 

Answers to the questions

1. To find the value of          

   Factorizing the denominators

   

   Since x+4 is a common factor in the denominator.

   




2. To find the value of          

   
   

   




3. To find the value of          

   
   

   




4. To find the value of          

   
   

   Factorizing the first terms denominator

   

   cancelling like terms

   




5. To find the value of          

   
   

   Factorizing the numerator and denominators