Question

Help would be much appreciated!​

Answer 1

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

Answer 2

• x = 5

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