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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.
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).
