Simplify the following expression: 12 x 4 y 36 x y

Given: 12 x 4 y 36 x y A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials. Let us factorize the numerator and denominator, ⇒ 2 × 2 × 3 × x y × x 3 2 × 2 × 3 × 3 × x y On cancelling common factors, ⇒ 2 × 2 × 3 × x y × x 3 2 × 2 × 3 × 3 × x y ⇒ x 3 3 Hence, the answer is x 3 3 .

Simplify the following : 5 x 7 - 6 x 5 4 x 3

Given: 5 x 7 - 6 x 5 4 x 3 ⇒ 5 x 7 4 x 3 - 6 x 5 4 x 3 A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials. Let us factorize the numerator and denominator, ⇒ 5 × x 3 × x 4 4 × x 3 - 2 × 2 × 2 × x 3 × x 2 2 × 2 × x 3 On cancelling common factors, ⇒ 5 × x 3 × x 4 4 × x 3 - 2 × 2 × 2 × x 3 × x 2 2 × 2 × x 3 ⇒ 5 x 4 4 - x 2 Hence, the answer is 5 x 4 4 - x 2 .

Simplify the following : x 2 - 4 x - 21 x 2 - 8 x - 33

Given: x 2 - 4 x - 21 x 2 - 8 x - 33 A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials. Let us factorize the numerator and denominator, ⇒ x 2 - 7 x + 3 x - 21 x 2 - 11 x + 3 x - 33 ⇒ x x - 7 + 3 x - 7 x x - 11 + 3 x - 11 ⇒ x - 7 x + 3 x - 11 x + 3 Cancelling the like factors, ⇒ x - 7 x - 11 Hence, the answer is x - 7 x - 11 .

Simplify the following : x + 4 x 2 - 16

Given: x + 4 x 2 - 16 A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials. Let us factorize the numerator and denominator, ⇒ x + 4 x 2 - 4 2 ⇒ x + 4 x + 4 x - 4 ∵ a 2 - b 2 = a + b a - b Cancelling the like factors, ⇒ 1 x - 4 Hence, the answer is 1 x - 4 .

Simplify the following : 2 x + y 5

Given: 2 x + y 5 A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials. If there is no common factor between the denominators then the LCM is simply the product of the denominators. ⇒ 2 x × 1 5 + y 5 × 1 x ⇒ 2 5 x + y 5 x Simplifying the answer completely, ⇒ 2 + y 5 x Hence, the answer is 2 + y 5 x .

Simplify the following : 16 x 3 y 2 5 z 3 × 15 z 8 x y

Given: 16 x 3 y 2 5 z 3 × 15 z 8 x y A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials. Let us factorize the numerator and denominator, ⇒ 8 × 2 × x × x 2 × y × y 5 × z × z 2 × 5 × 3 × z 8 × x × y Cancelling the like factors, ⇒ 8 × 2 × x × x 2 × y × y 5 × z × z 2 × 5 × 3 × z 8 × x × y ⇒ 2 x 2 y z 2 × 3 ⇒ 6 x 2 y z 2 Hence, the answer is 6 x 2 y z 2 .

Simplify the following : x 3 y 2 + x 2 y 3 x 3 y 3 ÷ x 2 - y 2 x 4 y 4

Given: x 3 y 2 + x 2 y 3 x 3 y 3 ÷ x 2 - y 2 x 4 y 4 ⇒ x 3 y 2 + x 2 y 3 x 3 y 3 × x 4 y 4 x 2 - y 2 A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quotient of polynomials. Let us factorize the numerator and denominator, ⇒ x 2 y 2 x + y x 2 y 2 × x y × x y × x 3 y 3 x + y x - y Cancelling the like factors, ⇒ x 2 y 2 x + y x 2 y 2 × x y × x y × x 3 y 3 x + y x - y ⇒ x 3 y 3 x - y Hence, the answer is x 3 y 3 x - y .