# Rational Algebraic Expressions

## Definition

• Rational algebraic expressions: If A and B are two algebraic expressions then "A"/"B" is called a rational algebraic.

## Notes

### Rational algebraic expressions:

• If A and B are two algebraic expressions then "A"/"B" is called a rational algebraic expression.
• While simplifying a rational algebraic expression, we have to perform operations of addition, subtraction, multiplication, and division.

## Example

Simplify: (a^2 + 5a + 6)/(a^2 - a - 12) xx (a - 4)/(a^2 - 4)

(a^2 + 5a + 6)/(a^2 - a - 12) xx (a - 4)/(a^2 - 4)

= ((a + 3)(a + 2))/((a - 4)(a + 3)) xx (a - 4)/((a + 2)(a - 2))

= 1/(a - 2)

## Example

Simplify: (7x^2 + 18x + 8)/(49x^2 - 16) xx (14x - 8)/(x + 2)

(7x^2 + 18x + 8)/(49x^2 - 16) xx (14x - 8)/(x + 2)

= ((7x + 4)(x + 2))/((7x + 4)(7x - 4)) xx (2(7x - 4))/(x + 2)

= 2

## Example

Simplify: (x^2 - 9y^2)/(x^3 - 27y^3).

(x^2 - 9y^2)/(x^3 - 27y^3).

= ((x + 3y)(x - 3y))/((x - 3y)(x^2 + 3xy + 9y^2))

= (x + 3y)/(x^2 + 3xy + 9y^2)

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