Multiply the following algebraic fractions. ( x - 2 ) ( x - 3 ) ( x + 2 ) ( x + 3 ) × ( x + 1 ) ( x + 2 ) ( x - 1 ) ( x - 2 ) , x ∉ { - 3 , 1 , ± 2 } .

Given that, we have ( x - 2 ) ( x - 3 ) ( x + 2 ) ( x + 3 ) × ( x + 1 ) ( x + 2 ) ( x - 1 ) ( x - 2 ) , x ∉ { - 3 , 1 , ± 2 } Therefore, we can write it as ( x - 2 ) ( x - 3 ) ( x + 2 ) ( x + 3 ) × ( x + 1 ) ( x + 2 ) ( x - 1 ) ( x - 2 ) = ( x - 2 ) ( x + 2 ) ( x - 2 ) ( x + 2 ) × ( x - 3 ) ( x + 1 ) ( x + 3 ) ( x - 1 ) = ( x - 2 ) ( x + 2 ) ( x - 2 ) ( x + 2 ) × ( x - 3 ) ( x + 1 ) ( x + 3 ) ( x - 1 ) [Cancelling the common factors in the numerator and denominator] = x 2 + x - 3 x - 3 x 2 - x + 3 x - 3 = x 2 - 2 x - 3 x 2 + 2 x - 3 Hence, the required expression is x 2 - 2 x - 3 x 2 + 2 x - 3 .

Multiply the following algebraic fractions. x 2 + 3 x - 4 2 x 2 - 14 x + 24 × 4 x 2 - 16 x + 12 2 x 2 + 4 x - 16 , x ∉ 2 , 3 , ± 4 .

Given that, we have x 2 + 3 x - 4 2 x 2 - 14 x + 24 × 4 x 2 - 16 x + 12 2 x 2 + 4 x - 16 , x ∉ 2 , 3 , ± 4 Therefore, we can write it as x 2 + 3 x - 4 2 x 2 - 14 x + 24 × 4 x 2 - 16 x + 12 2 x 2 + 4 x - 16 = x 2 + 3 x - 4 2 x 2 - 7 x + 12 × 4 x 2 - 4 x + 3 2 x 2 + 2 x - 8 = x 2 + 3 x - 4 4 x 2 - 7 x + 12 × 4 x 2 - 4 x + 3 x 2 + 2 x - 8 [Cancelling the common factors in the numerator and denominator] = x 2 + 3 x - 4 x 2 - 7 x + 12 × x 2 - 4 x + 3 x 2 + 2 x - 8 = x 2 + 4 x - x - 4 x 2 - 4 x - 3 x + 12 × x 2 - 3 x - x + 3 x 2 + 4 x - 2 x - 8 = x + 4 x - 1 x - 4 x - 3 × x - 3 x - 1 x + 4 x - 2 = x + 4 x - 1 x - 4 x - 3 × x - 3 x - 1 x + 4 x - 2 [Cancelling the common factors in the numerator and denominator] = x - 1 2 x - 4 x - 2 = x 2 - 2 x + 1 x 2 - 4 x - 2 x - 8 = x 2 - 2 x + 1 x 2 - 6 x - 8 Hence, the required expression is x 2 - 2 x + 1 x 2 - 6 x - 8 .

Divide the following fractions, and write your answer in the simplest form. ( x - 8 ) ( x - 2 ) x ( x + 4 ) ( x + 3 ) ÷ x ( x + 4 ) ( x - 2 ) ( x + 3 ) ( x - 5 ) , x ∉ - 4 , - 3 , 0 , 2 , 5 .

Given that, we have ( x - 8 ) ( x - 2 ) x ( x + 4 ) ( x + 3 ) ÷ x ( x + 4 ) ( x - 2 ) ( x + 3 ) ( x - 5 ) , x ∉ - 4 , - 3 , 0 , 2 , 5 Therefore, we can write it as ( x - 8 ) ( x - 2 ) x ( x + 4 ) ( x + 3 ) ÷ x ( x + 4 ) ( x - 2 ) ( x + 3 ) ( x - 5 ) = ( x - 8 ) ( x - 2 ) x ( x + 4 ) ( x + 3 ) × ( x + 3 ) ( x - 5 ) x ( x + 4 ) ( x - 2 ) [To divide by a fraction, multiply by its reciprocal] = ( x - 8 ) ( x - 2 ) x ( x + 4 ) ( x + 3 ) × ( x + 3 ) ( x - 5 ) x ( x + 4 ) ( x - 2 ) [Cancelling the common factors in the numerator and denominator] = ( x - 8 ) x ( x + 4 ) × ( x - 5 ) x ( x + 4 ) = ( x - 8 ) ( x - 5 ) x ( x + 4 ) x ( x + 4 ) = ( x 2 - 8 x - 5 x + 40 ) x 2 ( x + 4 ) 2 = ( x 2 - 13 x + 40 ) x 2 x 2 + 8 x + 16 = x 2 - 13 x + 40 x 4 + 8 x 3 + 16 x 2 Hence, the simplest form of ( x - 8 ) ( x - 2 ) x ( x + 4 ) ( x + 3 ) ÷ x ( x + 4 ) ( x - 2 ) ( x + 3 ) ( x - 5 ) , x ∉ - 4 , - 3 , 0 , 2 , 5 is x 2 - 13 x + 40 x 4 + 8 x 3 + 16 x 2 .

Divide the following fractions, and write your answer in the simplest form. x 2 + 3 x - 4 2 x 2 - 14 x + 24 ÷ 4 x 2 - 16 x + 12 2 x 2 + 4 x - 16 , x ∉ - 4 , 1 , 2 , 3 , 4 .

Given that, we have x 2 + 3 x - 4 2 x 2 - 14 x + 24 ÷ 4 x 2 - 16 x + 12 2 x 2 + 4 x - 16 , x ∉ - 4 , 1 , 2 , 3 , 4 Therefore, we can write it as x 2 + 3 x - 4 2 x 2 - 14 x + 24 ÷ 4 x 2 - 16 x + 12 2 x 2 + 4 x - 16 = x 2 + 3 x - 4 2 x 2 - 14 x + 24 × 2 x 2 + 4 x - 16 4 x 2 - 16 x + 12 [To divide by a fraction, multiply by its reciprocal] = x 2 + 3 x - 4 2 x 2 - 7 x + 12 × 2 x 2 + 2 x - 8 4 x 2 - 4 x + 3 = x 2 + 3 x - 4 2 x 2 - 7 x + 12 × 2 x 2 + 2 x - 8 4 x 2 - 4 x + 3 [Cancelling the common factors in the numerator and denominator] = x 2 + 3 x - 4 x 2 + 2 x - 8 4 x 2 - 7 x + 12 x 2 - 4 x + 3 = x 2 + 4 x - x - 4 x 2 + 4 x - 2 x - 8 4 x 2 - 4 x - 3 x + 12 x 2 - 3 x - x + 3 = x + 4 x - 1 x + 4 x - 2 4 x - 4 x - 3 x - 3 x - 1 = x + 4 x - 1 x + 4 x - 2 4 x - 4 x - 3 x - 3 x - 1 [Cancelling the common factors in the numerator and denominator] = x + 4 2 x - 2 4 x - 4 x - 3 2 = x 2 + 8 x + 16 x - 2 4 x - 4 x 2 - 6 x + 9 = x 3 + 8 x 2 + 16 x - 2 x 2 - 16 x - 32 4 x 3 - 6 x 2 + 9 x - 4 x 2 + 24 x - 36 = x 3 + 6 x 2 - 32 4 x 3 - 10 x 2 + 23 x - 36 = x 3 + 6 x 2 - 32 4 x 3 - 40 x 2 + 92 x - 144 Hence, the simplest form of x 2 + 3 x - 4 2 x 2 - 14 x + 24 ÷ 4 x 2 - 16 x + 12 2 x 2 + 4 x - 16 , x ∉ - 4 , 1 , 2 , 3 , 4 is x 3 + 6 x 2 - 32 4 x 3 - 40 x 2 + 92 x - 144 .

E M B I B E

Extended MYP Mathematics A Concept based approach Years 4 & 5>What Comes Next?>Chapter 11 - Rational Algebraic Expressions>Exploration 2

Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 7: Exploration 2

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 7: Exploration 2

Attempt the free practice questions from Exercise 7: Exploration 2 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.