what exactly is addition and subtraction of rational expressions?

Question

Can someone define and give me examples.

Answer 1

A "rational expression" is a fraction in which the numerator and denominator are polynomials. For instance,

( x + 2 ) / ( 2x - 3 ) and ( 3x - 3 ) / ( x + 1 )

are rational expressions.

To add or subtract them, you first give them common denominators. For instance, say you desire to add the above expressions:

( x + 2 ) / ( 2x - 3 ) + ( 3x - 3 ) / ( x + 1 )

Give them a common denominator:

( x + 2 ) ( x + 1 ) / ( 2x - 3 ) ( x + 1 ) + ( 3x - 3 ) ( 2x - 3 ) / ( x + 1 ) ( 2x - 3 )

Now add the numerators:

[ ( x + 2 ) ( x + 1 ) + ( 3x - 3 ) ( 2x - 3 ) ] / ( 2x - 3 ) ( x + 1 )

Further simplification is left as an exercise for the reader :)