While exploring an abandoned mountain fortress, Emek and Tara found a network of locked passages controlled by panels displaying algebraic fractions. Each intersection offered several routes, but only the passage connected to the correctly simplified expression would open. They compared different factorization methods, identified common factors in the numerators and denominators, and simplified each expression while checking that no invalid cancellations were made. Their efficient work revealed the correct sequence of passages through the fortress. At the end of the maze, they recovered a valuable historical artifact that had remained hidden for centuries.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Factor the numerator before canceling the common factor.
One fortress panel displays the expression (x² + 5x)/(x). Which simplified expression opens the correct passage?
x + 5x² + 55x - 5
Correct! Factor the numerator as x(x + 5), then cancel the common factor x (with x ≠ 0).
Factor the numerator first and only cancel common factors.
Next
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Hint
Determine when the denominator equals zero.
A second panel shows (x² - 36)/(x - 6). How many integer values of x from 4 through 8 are not allowed because the original denominator is zero?
Correct! Only one integer in the interval makes the denominator zero.
Check which value of x makes x - 6 equal to zero.
Next
🎉 Congrats! You got this question!
Hint
Factor the numerator and remember to keep any restrictions from the original expression.
Emek and Tara compare two simplifications of (x² - x - 6)/(x - 3). Student A says the result is x + 2. Student B says the result is x + 2 with the restriction x ≠ 3. Who is correct?
Student A onlyStudent B onlyBoth students are correctNeither student is correct
Correct! The simplified expression is x + 2, but the original expression is undefined when x = 3.
Do not forget that the original denominator determines any excluded values.
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🎉 Congrats! You finished this challenge set!
Kale Geçitleri
TR
ARC_G10_FRD_01_STORY_02
Kale Geçitleri
The Fortress Passage
EN
ARC_G10_FRD_01_STORY_02
The Fortress Passage