Rational Expressions Involving Addition and Subtraction

# Rational Expressions Involving Addition and Subtraction

## How to Solve Rational Expressions Involving Addition and Subtraction?

To Add or Subtract Rational Numbers with the Same Denominator you just need to add/subtract numerators from each other. If the Denominators aren’t the same in the Expressions you need to find a Common Denominator. The Simplest way is to multiply the Denominators with each other. However, this might not have the simplest computations and needs further simplifying afterward.

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One way of making computations easier is to find the LCD i.e. common multiple of two or more numbers present.

### Solved Examples

1. Simplify the Rational Expression x/(x+1)+2/(x+1)?

Solution:

Since the Rational Expression has common denominators we can simply add the numerators of each other while keeping the denominators unchanged.

= x/(x+1)+2/(x+1)

= (x+2)/(x+1)

Therefore, x/(x+1)+2/(x+1) on simplifcation will result in (x+2)/(x+1).

2. Simplify Rational Expression 3/(x+1)+2/(x-1)?

Solution:

Since both the denominators aren’t equal we need to find out the LCD. Simply multiply the denominators.

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

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

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

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

= (5x-1)/(x+1)(x-1)

Therefore, 3/(x+1)+2/(x-1) on simplifying gives (5x-1)/(x+1)(x-1).

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