Emek and Tara arrived at a suspension bridge stretching across a deep canyon, where each checkpoint was protected by a locked gate. Instead of keys, the control panels displayed algebraic fractions that had to be simplified before the next section of the bridge would open. They carefully factored expressions, canceled common factors only when valid, and checked for any restrictions on variable values before confirming each simplified result. Every correct simplification unlocked another gate, allowing them to move safely across the bridge. After solving the final expression, they reached the opposite side and continued their expedition with confidence.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
Factor the numerator before canceling any common factor.
To unlock the first bridge gate, Emek and Tara simplify the algebraic fraction (x² - 9)/(x - 3). Which simplified expression is correct?
x + 3x - 3x² + 31
Correct! Factor x² - 9 = (x - 3)(x + 3), then cancel the common factor.
Factor the numerator first and only cancel common factors.
Next
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Hint
Find when the denominator equals zero.
For the expression (x² - 16)/(x - 4), how many integer values of x from 1 through 6 are not allowed because the original denominator is zero?
Correct! Only one integer in the given range makes the denominator zero.
Check which value of x makes x - 4 equal to zero.
Next
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Hint
Remember that simplifying does not remove restrictions from the original expression.
Which statement about simplifying (x² - 25)/(x - 5) is correct?
The simplified expression is x + 5 for all real numbers.The simplified expression is x + 5, but x cannot equal 5.The simplified expression is x - 5.No simplification is possible.
Correct! The expression simplifies to x + 5, but x = 5 is still excluded.
Factor the numerator and keep the original domain restriction.
Next
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🎉 Congrats! You finished this challenge set!
Kanyon Geçişi
TR
ARC_G10_FRD_01_STORY_01
Kanyon Geçişi
The Canyon Crossing
EN
ARC_G10_FRD_01_STORY_01
The Canyon Crossing