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McGraw Hill Glencoe Algebra 1, 2012

MH

McGraw Hill Glencoe Algebra 1, 2012 View details

4. Radical Equations

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Exercise 39 Page 646

We are given four options, each including a fraction with the variable $w .$ Among these options we will find the one that is undefined when $w = 3 .$ Recall that if the denominator of a fraction is zero, the expression is undefined. Let's now substitute $w = 3$ into each fraction and solve.

Option	Fraction	Substitution	Result
A	$\frac{w - 3}{w + 1}$	$\frac{3 - 3}{3 + 1} = \frac{0}{4}$	$0$
B	$\frac{w ^{2} - 3 w}{3 w}$	$\frac{3 ^{2} - 3 ( 3 )}{3 ( 3 )} = \frac{0}{9}$	$0$
C	$\frac{w + 1}{w ^{2} - 3 w}$	$\frac{3 + 1}{3 ^{2} - 3 ( 3 )} = \frac{4}{0}$	$Undefined$
D	$\frac{3 w}{3 w ^{2}}$	$\frac{3 ( 3 )}{3 ( 3 ) ^{2}} = \frac{9}{2 7}$	$\frac{1}{3}$

As we can see from the table, the denominator of the fraction in option C becomes $0$ when $w$ is equal to $3 .$ This means that this fraction is undefined when $w = 3 .$ To see a step-by-step explanation for these calculations, please see the bottom of this solution.

Showing Our Work

Substitution

Let's explain the calculations in the substitutions step-by-step. We will start with the option A and substitute

w = 3

into the fraction

\frac{w - 3}{w + 1} .

\frac{w - 3}{w + 1}

$w = 3$

\frac{3 - 3}{3 + 1}

Add and subtract terms

\frac{0}{4}

$\frac{0}{a} = 0$

0

As we can see, the expression is equal to

0

when

w = 3 .

Now, let's substitute

w = 3

into the fraction in option B.

\frac{w ^{2} - 3 w}{3 w}

$w = 3$

\frac{3 ^{2} - 3 ( 3 )}{3 ( 3 )}

Calculate power

\frac{9 - 3 ( 3 )}{3 ( 3 )}

Multiply

\frac{9 - 9}{9}

Subtract term

\frac{0}{9}

$\frac{0}{a} = 0$

0

We can see that the expression becomes

0

when

w = 3 .

We will now substitute

w = 3

into the fraction in option C.

\frac{w + 1}{w ^{2} - 3 w}

$w = 3$

\frac{3 + 1}{3 ^{2} - 3 ( 3 )}

Calculate power

\frac{3 + 1}{9 - 3 ( 3 )}

Multiply

\frac{3 + 1}{9 - 9}

Add and subtract terms

\frac{4}{0}

Notice that the denominator of the fraction in option C is

0 .

It means that it is undefined when

w = 3 .

Finally, let's substitute

w = 3

into the fraction in option D.

\frac{3 w}{3 w ^{2}}

$w = 3$

\frac{3 ( 3 )}{3 ( 3 ) ^{2}}

Calculate power

\frac{3 ( 3 )}{3 ( 9 )}

Multiply

\frac{9}{2 7}

$\frac{a}{b} = \frac{a / 9}{b / 9}$

\frac{1}{3}

As we can see, the fraction in option D is

\frac{1}{3}

when

w = 3 .

Subchapter links

Check Your Understanding p.644

H.O.T. Problems p.645

Standardized Test Practice p.646

Skills Review p.646