## 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. 2. 3. 4. 5. 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 