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2:22pm mon feb 9 m317 cs unit 5b rationals part 2 test s fill in the bl…

$x=5,x=-2$

分類: calculus 更新時間: 2026-02-09

題目

2:22pm mon feb 9
m317 cs unit 5b rationals part 2 test s
fill in the blank.
question 7
find the following given the function. no spaces in answers.
$y = \\frac{x - 2}{x^2 - 3x - 10}$
vertical asymptote:

解題步驟

  1. Understand the question

    2:22pm mon feb 9
    m317 cs unit 5b rationals part 2 test s
    fill in the blank.
    question 7
    find the following given the function. no spaces in answers.
    $y = \\frac{x - 2}{x^2 - 3x - 10}$
    vertical asymptote:

  2. Explanation

    Step1: Factor the denominator

    $x^2-3x-10=(x-5)(x+2)$

    Step2: Identify undefined x-values

    Set denominator to 0: $(x-5)(x+2)=0$
    Solutions: $x=5$, $x=-2$

    Step3: Check for removable factors

    Numerator is $x-2$, no common factors with denominator.

    Step4: Confirm vertical asymptotes

    Vertical asymptotes are at non-removable undefined x-values.

  3. Final answer

    $x=5,x=-2$

答案

Explanation

Step1: Factor the denominator

$x^2-3x-10=(x-5)(x+2)$

Step2: Identify undefined x-values

Set denominator to 0: $(x-5)(x+2)=0$
Solutions: $x=5$, $x=-2$

Step3: Check for removable factors

Numerator is $x-2$, no common factors with denominator.

Step4: Confirm vertical asymptotes

Vertical asymptotes are at non-removable undefined x-values.

Answer

$x=5,x=-2$

Question Image

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Question Analysis

Subject mathematics
Sub Subject calculus
Education Level high school
Difficulty unspecified
Question Type with image, calculation
Multi Question No
Question Count 1
Analysis Status completed
Analyzed At 2026-02-09T20:22:31

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2:22pm mon feb 9
m317 cs unit 5b rationals part 2 test s
fill in the blank.
question 7
find the following given the function. no spaces in answers.
$y = \\frac{x - 2}{x^2 - 3x - 10}$
vertical asymptote:

相關知識點

mathematicscalculuswith image, calculationhigh schoolturns-1

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