SenorMathWizidn
Answered

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Mhanifaidn

Answer:

  • x = 5

Step-by-step explanation:

A hole is an input value that makes both numerator and denominator equal to zero.

In other words, same factor in both numerator and denominator.

Let's factorize the denominator:

  • x² - 7x + 10 = x² - 5x - 2x +  10 = x(x - 5) - 2(x - 5) = (x - 2)(x - 5)

We have same factor of x - 5:

  • x - 5 = 0
  • x = 5 is a hole

Factor the denominator taking 0

  • x²-7x+10=0
  • (x-2)(x-5)=0
  • x={2,5}

Factor numerator

  • x-5=0
  • x=5

x =5 is common so a hole at x=5

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