Solve Rational Equations

Rational equations and extraneous solutions. In MathBound, the free Algebra I adventure game, Trapdoor Tess asks these problems, and the only way past is to solve them.

Part of More topics: taught by some textbooks beyond the usual course.

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10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Solve Rational Equations. Solve a rational equation with monomial denominators by multiplying every term by the LCD to clear fractions.
Identify Extraneous Solutions. Solve a rational equation and identify/reject apparent solutions that cause division by zero in the original equation.
Solve for a Specific Variable. Solve a literal equation or formula for a specified variable located in the numerator.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Solve Rational Equations

Solve:

\frac{x}{6} + \frac{x}{4} = 10

$x = 120$
$x = 60$
$x = 24$
$x = 100$

Show the worked steps

$Multiply$ $every$ $term$ $by$ $the$ $LCD$ $12 : 2 x + 3 x = 120 .$
$5 x = 120,$ $so$ $x = 24 .$

Answer: $x = 24$

Example 2 · Identify Extraneous Solutions

Clearing

the

fractions

in

\frac{x ^{2}}{x - 7} = \frac{8 x - 7}{x - 7}

gives

x = 1

or

x = 7 .

Which

is

extraneous?

$Neither$
$x = 1$
$Both$
$x = 7$

Show the worked steps

$A$ $root$ $is$ $extraneous$ $when$ $it$ $makes$ $a$ $denominator$ $of$ $the$ $original$ $equation$ $zero.$
$x = 7$ $makes$ $x - 7$ $zero;$ $x = 1$ $does$ $not,$ $so$ $x = 7$ $is$ $extraneous.$

Answer: $x = 7$

Example 3 · Solve for a Specific Variable

Solve

V = \frac{B h}{3}

for

B .

$B = \frac{V h}{3}$
$B = \frac{3 V}{h}$
$B = \frac{3 h}{V}$
$B = \frac{V}{3 h}$

Show the worked steps

$Multiply$ $both$ $sides$ $by$ $3 : 3 V = B h .$
$Divide$ $by$ $h : B = \frac{3 V}{h} .$

Answer: $B = \frac{3 V}{h}$

Where it is in your textbook

Textbook	Lessons
CPM Core Connections Algebra	10.2.2
CPS Skyline Algebra	4.2-4.3
Eureka Math Algebra I (EngageNY)	1.17-1.19
Glencoe Algebra 1	11-8
OpenStax Elementary Algebra 2e	8.6, 8.8
Pearson Algebra 1 Common Core	11-5

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