body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Core Connections Algebra 2, 2013

CC

Core Connections Algebra 2, 2013 View details

2. Section 3.2

Finish the assignment

Continue to next subchapter

Exercise 107 Page 154

Practice makes perfect

a

When multiplying two fractions the numerator and denominator can be multiplied separately. Then we can factor out a Giant One.

(3x-1)(x+7)/4(2x-5)*10(2x-5)/(4x+1)(x+7)

Multiply fractions

(3x-1)(x+7)* 10(2x-5)/4(2x-5)(4x+1)(x+7)

CommutativePropMult

Commutative Property of Multiplication

10(3x-1)(x+7)(2x-5)/4(4x+1)(x+7)(2x-5)

Write as a product of fractions

10(3x-1)/4(4x+1)*(x+7)(2x-5)/(x+7)(2x-5)

a/a=1

10(3x-1)/4(4x+1)*1

Identity Property of Multiplication

10(3x-1)/4(4x+1)

a/b=.a /2./.b /2.

5(3x-1)/2(4x+1)

b

Let's start by simplifying the numerator and denominator separately.

(m-3)(m+11)/(2m+5)(m-3)÷(4m-3)(m+11)/(4m-3)(2m+5)

CommutativePropMult

Commutative Property of Multiplication

(m-3)(m+11)/(m-3)(2m+5)÷(4m-3)(m+11)/(4m-3)(2m+5)

Write as a product of fractions

(m-3/m-3*m+11/2m+1)÷(4m-3/4m-3*m+11/2m+5)

a/a=1

(1*m+11/2m+1)÷(1*m+11/2m+5)

Identity Property of Multiplication

m+11/2m+5÷m+11/2m+5

To divide fractions, we take the reciprocal of the second fraction and multiply them together. m+11/2m+5÷m+11/2m+5 [0.5em] ⇕ [0.5em] m+11/2m+5*2m+5/m+11 Look at the numerator and denominator of the fractions — they're the same. Therefore, this expression can be simplified to 1.

c

We have another expression to multiply. To simplify, let's factor all polynomials before we multiply.

2p^2+5p-12/2p^2-5p+3*p^2+8p-9/3p^2-10p-8 Let's factor the first one.

2p^2+5p-12

▼

Factor

Write as a difference

2p^2+8p-3p-12

Factor out 2p

2p(p+4)-3p-12

Factor out 3

2p(p+4)-3(p+4)

Factor out (p+4)

(2p-3)(p+4)

The numerator of the first fraction can be simplified to (2p-3)(p+4).

(2p-3)(p+4)/2p^2-5p+3*p^2+8p-9/3p^2-10p-8 Let's factor the second.

2p^2-5p+3

▼

Factor

Write as a difference

2p^2-2p-3p+3

Factor out 2p

2p(p-1)-3p+3

Factor out 3

2p(p-1)-3(p-1)

Factor out (p-1)

(2p-3)(p-1)

The factored form of the denominator in the first fraction is (2p-3)(p-1). (2p-3)(p+4)/(2p-3)(p-1)*p^2+8p-9/3p^2-10p-8 Let's factor the third.

p^2+8p-9

▼

Factor

Write as a difference

p^2+9p-p-9

Factor out p

p(p+9)-p-9

FactorOutNegSign

Factor out a minus sign

p(p+9)-(p+9)

Factor out (p+9)

(p-1)(p+9)

In the second fraction, the numerator can be factored to (p-1)(p+9). (2p-3)(p-1)/(2p-3)(p-1)*(p-1)(p+9)/3p^2-10p-8 Let's factor the fourth.

3p^2-10p-8

▼

Factor

Write as a difference

3p^2+12p-2p-8

Factor out 3p

3p(p+4)-2p-8

Factor out 2

3p(p+4)-2(p+4)

Factor out (p+4)

(3p-2)(p+4)

Now we have the factored forms. (2p-3)(p-1)/(2p-3)(p-1)*(p-1)(p+9)/(3p-2)(p+4) Let's simplify this.

(2p-3)(p+4)/(2p-3)(p-1)*(p-1)(p+9)/(3p-2)(p+4)

Multiply fractions

(2p-3)(p+4)(p-1)(p+9)/(2p-3)(p-1)(3p-2)(p+4)

CommutativePropMult

Commutative Property of Multiplication

(2p-3)(p+4)(p-1)(p+9)/(2p-3)(p+4)(p-1)(3p-2)

Write as a product of fractions

(2p-3)(p+4)(p-1)/(2p-3)(p+4)(p-1)* p+9/3p-2

a/a=1

1* p+9/3p-2

Identity Property of Multiplication

p+9/3p-2

d

We have one more fraction to divide.

4x-12/x^2+3x-10÷2x^2-13x+21/2x^2+3x-35 Looking at the equation, we can tell that the numerator in the first fraction can be factored as 4x-12 = 4(x-3). Now let's factor the rest of the polynomials. 4(x-3)/x^2+3x-10÷2x^2-13x+21/2x^2+3x-35Let's factor the first expression.

x^2+3x-10

▼

Factor

Write as a difference

x^2+5x-2x-10

Factor out x

x(x+5)-2x-10

Factor out 2

x(x+5)-2(x+5)

Factor out (x+5)

(x-2)(x+5)

The denominator in the first fraction is (x-2)(x+5). 4(x-3)/(x-2)(x+5)÷2x^2-13x+21/2x^2+3x-35 Let's factor the second expression.

2x^2-13x+21

▼

Factor

Write as a difference

2x^2-6x-7x+21

Factor out 2x

2x(x-3)-7x+21

Factor out 7

2x(x-3)-7(x-3)

Factor out (x-3)

(2x-7)(x-3)

The numerator in the second fraction can be factored to (2x-7)(x-3). 4(x-3)/(x-2)(x+5)÷(2x-7)(x-3)/2x^2+3x-35 Let's factor the third expression.

2x^2+3x-35

▼

Factor

Write as a difference

2x^2+10x-7x-35

Factor out 2x

2x(x+5)-7x-35

Factor out 7

2x(x+5)-7(x+5)

Factor out (x+5)

(2x-7)(x+5)

Now we have the factored form. 4(x-3)/(x-2)(x+5)÷(2x-7)(x-3)/(2x-7)(x+5) Let's simplify this.

4(x-3)/(x-2)(x+5)÷(2x-7)(x-3)/(2x-7)(x+5)

Write as a product of fractions

4(x-3)/(x-2)(x+5)÷(2x-7/2x-7*x-3/x+5)

a/a=1

4(x-3)/(x-2)(x+5)÷(1*x-3/x+5)

Identity Property of Multiplication

4(x-3)/(x-2)(x+5)÷x-3/x+5

DivFracByFracDiv

a/b÷c/d=a/b*d/c

4(x-3)/(x-2)(x+5)*x+5/x-3

Multiply fractions

4(x-3)(x+5)/(x-2)(x+5)(x-3)

CommutativePropMult

Commutative Property of Multiplication

4(x-3)(x+5)/(x-2)(x-3)(x+5)

Write as a product of fractions

4/x-2*(x-3)(x+5)/(x-3)(x+5)

a/a=1

4/x-2*1

Identity Property of Multiplication

4/x-2

Subchapter links

3.2.1 Investigating Rational Functions p.140-141

3.2.2 Simplifying Rational Expressions p.145-146

3.2.3 Multiplying and Dividing Rational Expressions p.148-149

3.2.4 Adding and Subtracting Rational Expressions p.153-154

3.2.5 Creating New Functions p.157-159