Addition of Rational Expression

Numbers which can be expressed in form of p / q where p and q are integers and q < > 0 are called rational numbers.  Rational expressions are the  expressions which consists of rational numbers. Various mathematical Operation on Rational Expression can be done like addition, subtraction, multiplication and division. We can do all operations on Rational numbers.
On doing addition of Rational Expressions, the output is also a rational number. In order to do Addition of Rational Expression, we first need to make the denominators of the operands same. For this we will first take the L.C.M. of all the denominators given in the expression. Then we try to replace all the denominators with the L.C.M.
For this we multiply both numerator and the denominator with some of the factors of the denominator, so that the denominator is the L.C.M. now. Then we proceed to the addition of the numerators, keeping the denominators same.
Let us look at the example:
Solve the given Rational Expression:   2 +  4/5  + (-3/10)
 Here we observe the three denominators are 1, 5 and 10. L.C.M. of these three numbers is 10.
So to make the denominator of 2 as 10, we multiply num. and denominator by 10
To make the denominator of  (4/5 ) as 10, we multiply both numerator and denominator by 2 and
 ( -3 / 10 ) already has 10 as the denominator.
Now we proceed:
 = 2 +  4/5  + (-3/10)
 = 2 *10/10   + ( 4 * 2 ) / (5 * 2 )   + ( -3 /10)
= 20 /10   + 8 /10 + (-3 /10 )
 = ( 20 + 8 -3 ) / 10
= 25 /10
= 5 / 2 Ans.

This is all about addition of rational numbers. In the nest article we will deal with Division of Rational Expressions.