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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 (Common 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

Add Rational Expressions. Add two rational expressions with a common denominator and combine like terms in the numerator.
Subtract Rational Expressions. Subtract rational expressions with a common denominator and monomial numerators.
Opposite Denominators. Add or subtract rational expressions where denominators are exact opposites by multiplying one expression by -1/-1.

Worked examples

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

Example 1 · Add Rational Expressions

Add:

\frac{3 x ^{2} - 4 x + 3}{x ^{2} + 1} + \frac{3 x ^{2} + x + 1}{x ^{2} + 1}

$\frac{6 x ^{2} - 3 x + 4}{x ^{2} + 1}$
$\frac{- 5 x + 2}{x ^{2} + 1}$
$\frac{6 x ^{2} - 3 x + 4}{2 x ^{2} + 2}$
$\frac{6 x ^{2} - 3 x + 2}{x ^{2} + 1}$

Show the worked steps

$Same$ $denominator:$ $add$ $the$ $numerators,$ $collecting$ $like$ $terms.$
$x^{2} : 6; x : - 3;$ $constant:$ $4 .$

Answer: $\frac{6 x ^{2} - 3 x + 4}{x ^{2} + 1}$

Example 2 · Subtract Rational Expressions

What

numerator

makes

this

true:

\frac{14 x}{x + 1} - \frac{?}{x + 1} = \frac{13 x}{x + 1}

$- x$
$13 x$
$x$
$27 x$

Show the worked steps

$The$ $numerators$ $must$ $satisfy$ $14 x - ? = 13 x .$
$So$ $?$ $= 14 x - 13 x = x .$

Answer: $x$

Example 3 · Opposite Denominators

Add:

\frac{3}{x + 6} + \frac{1}{- 6 - x}

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

Show the worked steps

$- 6 - x$ $is$ $- x + 6 :$ $flip$ $the$ $sign$ $of$ $the$ $second$ $fraction.$
$3 - 1 = 2,$ $so$ $the$ $sum$ $is$ $\frac{2}{x + 6} .$

Answer: $\frac{2}{x + 6}$

Where it is in your textbook

Textbook	Lessons
Glencoe Algebra 1	11-6
OpenStax Elementary Algebra 2e	8.3
Pearson Algebra 1 Common Core	11-4
SpringBoard Algebra 1	28

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