What is a Rational Expression

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A rational expression is an expression which is written in the form of ‘p/q’ where ‘p’ and ‘q’ are any polynomial expressions except q ≠ 0. Hence a rational expression has a numerator and a denominator and the expression in the denominator should not be equal to ‘0’ because then the expression becomes undefined. Rational expressions are very commonly used in math and they can be added, subtracted, multiplied and divided and these expressions can be simplified or factored according to the given question as well.
 
Example 1: Simplify the given rational expression, (4x2)/ (2x) * (3x/5).

Given rational expression: (4x2/2x) * (3x/5)

Now in order to multiply the given two rational expressions, we multiply the expressions in the numerator’s

together and the expressions in the denominators together.

This gives: (4x2 * 3x)/ (2x * 5) = 12x3/ 10x.

Now we can simplify the above expression by dividing the numerator and the denominator with their common
factor.

The common factor of 12 and 10 is ‘2’ and for ‘x3’ and ‘x’ is ‘x’.

Hence we get: 6x2/5.
 
Example 2: Simplify the given rational expression, (x2 – 16)/ (x – 4).

Given rational expression: (x2 – 16)/ (x – 4)

In order to simplify the above expression, we can factor the numerator.

According to the algebraic formula: a2– b2 = (a+ b) (a– b)

Now, we can write x2– 16 as x2– 42.

Applying the above formula we get, x2 – 42 = (x + 4) (x – 4)

Now (x2– 16)/ (x– 4) = (x+ 4) (x- 4)/ (x- 4).

Cancelling (x- 4) up and down, we get -> (x+ 4)

Therefore, (x2– 16)/ (x– 4) = (x+ 4)
 
 

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