Math - AtHomeTuition.com is a group of highly qualified and experienced tutors dedicated to provide students with world - class resources to help achieve their learning needs

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