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 : 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 .

Simplify the following : 7 x - 7 + 5 x + 5

Given: 7 x - 7 + 5 x + 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. ⇒ 7 x - 7 × 1 x + 5 + 5 x + 5 × 1 x - 7 ⇒ 7 x - 7 x + 5 + 5 x - 7 x + 5 Simplifying the answer completely, ⇒ 12 x - 7 x + 5 Hence, the answer is 12 x - 7 x + 5 .

Simplify the following : - 3 x + 9 + - 2 x - 8

Given: - 3 x + 9 + - 2 x - 8 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. ⇒ - 3 x + 9 × 1 x - 8 + - 2 x - 8 × 1 x + 9 ⇒ - 3 x + 9 x - 8 + - 2 x + 9 x - 8 Simplifying the answer completely, ⇒ - 5 x + 9 x - 8 Hence, the answer is - 5 x + 9 x - 8 .

Simplify the following : x + 1 x - 1 - x - 4 x + 4

Given: x + 1 x - 1 - x - 4 x + 4 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. ⇒ x + 1 x - 1 × 1 x + 4 - x - 4 x + 4 × 1 x - 1 ⇒ x + 1 x - 1 x + 4 - x - 4 x - 1 x + 4 Simplifying the answer completely, ⇒ x + 1 - x + 4 x - 1 x + 4 ⇒ 5 x - 1 x + 4 Hence, the answer is 5 x - 1 x + 4 .

Simplify the following : 9 x - 1 - 9 x - 4 x 2 - 1

Given: 9 x - 1 - 9 x - 4 x 2 - 1 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. ⇒ 9 x - 1 × 1 x 2 - 1 - 9 x - 4 x 2 - 1 × 1 x - 1 ⇒ 9 x - 1 x 2 - 1 - 9 x - 4 x - 1 x 2 - 1 Simplifying the answer completely, ⇒ 9 - 9 x + 4 x - 1 x + 1 x - 1 ⇒ 13 - 9 x x - 1 2 x + 1 Hence, the answer is 13 - 9 x x - 1 2 x + 1 .

Simplify the following : 3 a + 5 b - a + b 4

Given: 3 a + 5 b - a + b 4 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. ⇒ 3 a × 1 4 b + 5 b × 1 4 a - a + b 4 × 1 a b ⇒ 3 4 a b + 5 4 a b - a + b 4 a b Simplifying the answer completely, ⇒ 3 + 5 - a - b 4 a b ⇒ 8 - a - b 4 a b Hence, the answer is 8 - a - b 4 a b .

Simplify the following : x + 1 6 + 2 x - x x - 2

Given: x + 1 6 + 2 x - x x - 2 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. ⇒ x + 1 6 × 1 x x - 2 + 2 x × 1 6 x - 2 - x x - 2 × 1 6 x ⇒ x + 1 6 x x - 2 + 2 6 x x - 2 - x 6 x x - 2 Simplifying the answer completely, ⇒ x + 1 + 2 - x 6 x x - 2 ⇒ 3 6 x x - 2 ⇒ 1 2 x x - 2 Hence, the answer is 1 2 x x - 2 .

E M B I B E

Extended MYP Mathematics A Concept based approach Years 4 & 5>What Comes Next?>Chapter 11 - Rational Algebraic Expressions>Mixed practice

Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 15: Mixed practice

Author:Rose Harrison, Clara Huizink, Aidan Sproat Clements & Marlene Torres Skoumal

Rose Harrison Mathematics Solutions for Exercise - Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 15: Mixed practice

Attempt the free practice questions from Exercise 15: Mixed practice with hints and solutions to strengthen your understanding. Extended MYP Mathematics A Concept based approach Years 4 & 5 solutions are prepared by Experienced Embibe Experts.