Explain when you would use the LCM method to add two rationa

Explain when you would use the LCM method to add two rational expressions. Give two examples of adding two rational expressions, one in which you use the LCM and the other in which you do not.

Solution

LCM method should be used when we have different denominators. Addition of rational numbers is carried out in the same way as that with fractions.

Lets say, add -> 1.) 2/x + 3/x^2

LCM of x and x^2 will be x^2

Equation becomes 2x/x^2 + 3 /x^2

= 2x+3/x^2

2.) Add -> (2+x)/2x^2 + 3/4x

LCM will be 4x^2

= (2+x)(2)/4x^2 + 3x/4x^2

=4+2x+3x/4x^2

= 4+5x/4x^2

Now if the denominator is same, lets say add 4/2x + 6/2x

your answer is directly, 10/2x