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Elevator Ella

Elevator EllaFractioneers · rational expressions and functions

Brings everyone down to the same floor: adding and subtracting rational expressions.

Adding Rational Expressions (Unlike Denominators)

Adding and subtracting rational expressions. In MathBound, the free Algebra I adventure game, Elevator Ella 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

Find the LCD. Find the Least Common Denominator (LCD) for expressions with monomial denominators.
Build Equivalent Fractions. Rewrite a rational expression as an equivalent fraction with a newly determined LCD.
Add Rational Expressions. Add two rational expressions with unlike monomial denominators.
Subtract Rational Expressions. Subtract rational expressions with unlike polynomial denominators (requires distributing the negative).
Combined Operations. Add and subtract rational expressions requiring a common denominator with basic monomial terms.

Worked examples

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

Example 1 · Find the LCD

Find

the

LCD

of

\frac{5}{8 x y ^{2}}

and

\frac{7}{7 x y ^{2}} .

$x y^{2}$
$56 x y^{2}$
$168 x y^{2}$
$56 x^{2} y^{4}$

Show the worked steps

$Take$ $the$ $LCM$ $of$ $the$ $coefficients:$ $56 .$
$For$ $each$ $variable$ $take$ $the$ $LARGER$ $power.$

Answer: $56 x y^{2}$

Example 2 · Build Equivalent Fractions

Rewrite

\frac{7}{x + 6}

with

denominator

(x + 6) (x - 4) .

$\frac{x - 4}{( x + 6 ) ( x - 4 )}$
$\frac{7 x - 28}{( x + 6 ) ( x - 4 )}$
$\frac{7 x + 28}{( x + 6 ) ( x - 4 )}$
$\frac{7}{( x + 6 ) ( x - 4 )}$

Show the worked steps

$The$ $denominator$ $gains$ $a$ $factor$ $of$ $(x - 4),$ $so$ $the$ $numerator$ $must$ $too.$
$7 (x - 4) = 7 x - 28 .$

Answer: $\frac{7 x - 28}{( x + 6 ) ( x - 4 )}$

Example 3 · Add Rational Expressions

Add:

\frac{x - 1}{5} + \frac{x - 2}{6}

$\frac{11 x - 3}{30}$
$\frac{2 x - 3}{30}$
$\frac{2 x - 3}{11}$
$\frac{11 x - 16}{30}$

Show the worked steps

$The$ $LCD$ $is$ $30 :$ $multiply$ $the$ $tops$ $by$ $6$ $and$ $5 .$
$6 (x - 1) + 5 (x - 2) = 11 x - 16,$ $over$ $30 .$
$Reduced:$ $\frac{11 x - 16}{30} .$

Answer: $\frac{11 x - 16}{30}$

Where it is in your textbook

Textbook	Lessons
Glencoe Algebra 1	11-6, 11-7
OpenStax Elementary Algebra 2e	8.4
Pearson Algebra 1 Common Core	11-4
SpringBoard Algebra 1	28

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