In order to simplify Rational Expressions involving the Sum or Difference go through the complete article. Have a glance at the step by step procedure for solving Rational Expressions involving the Sum or Difference. The Solved Examples on Rational Numbers will help you get a good grip on the concept. By the end of this article, you can solve problems of Rational Expressions including the Sum or Difference on your own.

How to Simplify Rational Expressions Involving the Sum or Difference?

Follow the below-mentioned guidelines to solve Rational Expressions involving the sum or difference. They are along the lines

Step 1: Firstly, find the LCM of Denominators of all the Numbers Involved.

Step 2: Write the Rational Number whose denominator is the LCM obtained in the earlier step. For obtaining the numerator simply divide the LCM obtained with all the denominators of the rational numbers. Multiply the numerators of the respective rational numbers with the quotients you got. Keep the Addition, Subtraction Signs as it as in the Expressions. Simplify the Expression to get an Integer as Numerator.

Step 3: Reduce the Rational Number to its lowest or simplest form if it is not present. The Rational Number Obtained is the required Rational Number.

Solved Examples Simplifying Rational Expressions involving the Sum or Difference

1. Simplify -3/2 + 9/6 – (-5)/4?

Solution:

Given Expression is -3/2 + 9/6 – (-5)/4

= -3/2+9/6+5/4

Find the LCM of Denominators i.e. 2, 6, 4

LCM(2, 6, 4) = 12

Express the Rational Numbers using the LCM obtained in terms of a common denominator.

-3/2 = -3*6/2*6 = -18/12

9/6 = 9*2/6*2 = 18/12

5/4 = 5*3/4*3 = 15/12

Placing the Rational Numbers in the Expression we get

= -18/12+18/12+15/12

= 15/12

Therefore, -3/2 + 9/6 – (-5)/4 on simplifying gives a Rational Number 15/12.

2. Simplify 7/10 – (-5)/14 + 9/-3?

Solution:

Given Rational Expression is 7/10 – (-5)/14 + 9/-3

As One of the Denominators is negative we rearrange it to get a positive denominator.

9/-3 = 9*(-1)/-3*(-1) = -9/3

The Rational Expression becomes 7/10+5/14-9/3

Find the LCM of Denominators 10, 14, 3

LCM(10, 14,3) = 210

Express the Rational Numbers in terms of a Common Denominator using the LCM obtained.

7/10 = 7*21/10*21 = 147/210

5/14 = 5*15/14*15 = 75/210

-9/3 = -9*70/3*70 = -630/210

Placing the Rational Numbers in the Expression we get

= 147/210+75/210-630/210

= (147+75-630)/210

= -408/210

= -68/35

Therefore, on simplifying 7/10 – (-5)/14 + 9/-3 we get -68/35.