Simplify Rational Expressions

Simplifying rational expressions. In MathBound, the free Algebra I adventure game, Bunk-Bed Bot 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

Determine Undefined Values. Find the value(s) that make a rational expression undefined by setting a linear denominator to zero.
Evaluate Rational Expressions. Evaluate a rational expression for a given integer value.
Simplify Rational Expressions. Simplify a rational expression where the numerator and denominator are monomials using exponent rules.
Simplify Opposite Factors. Simplify a rational expression containing opposite binomial factors yielding -1.

Worked examples

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

Example 1 · Determine Undefined Values

For

what

value

of

x

is

\frac{6}{- 8 - x}

undefined?

$x = 0$
$x = 8$
$x = 6$
$x = - 8$

Show the worked steps

$Set$ $the$ $denominator$ $to$ $zero:$ $- 8 - x = 0.$
$So$ $x = - 8 .$

Answer: $x = - 8$

Example 2 · Evaluate Rational Expressions

Evaluate

\frac{6 x - 4}{x + 2}

when

x = 6 .

$32$
$4$
$\frac{1}{4}$
$8$

Show the worked steps

$Substitute$ $x = 6 :$ $top$ $32,$ $bottom$ $8 .$
$That$ $gives$ $4 .$

Answer: $4$

Example 3 · Simplify Rational Expressions

Simplify:

\frac{9 x ^{2} y ^{2}}{6 x y ^{3}}

$\frac{3 x ^{3}}{2 y ^{5}}$
$\frac{3 x}{2 y}$
$\frac{3 x y}{2}$
$\frac{2 x}{3 y}$

Show the worked steps

$Divide$ $the$ $coefficients,$ $then$ $each$ $variable$ $separately.$
$x : 2 - 1 = 1$ $on$ $top.$ $y : 3 - 2 = 1$ $below.$
$That$ $gives$ $\frac{3 x}{2 y} .$

Answer: $\frac{3 x}{2 y}$

Where it is in your textbook

Textbook	Lessons
Eureka Math Algebra I (EngageNY)	1.17-1.19
Glencoe Algebra 1	11-2, 11-3
OpenStax Elementary Algebra 2e	8.1
Pearson Algebra 1 Common Core	11-1, 11-7
SpringBoard Algebra 1	28

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