## Subtraction of Rational Expressions

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. 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