Maharashtra State BoardSSC (English Medium) 8th Standard

Rational Algebraic Expressions

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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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