Question

I have no idea what im doing

Answer 1

Factor denominator to 0

• x²+2x-24=0
• (x+6)(x-4)=0
• x={-6,4}

Factor numerator

• 3x²-108=0
• 3(x²-36)=0
• 3(x+6)(x-6)=0
• x={-6,6}

x=-6 is the hole as it's common

Answer 2

• x = - 6

Explanation:

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

Let's factorize the numerator and denominator:

• 3x² - 108 = 3(x² - 36) = 3(x + 6)(x - 6)
• x² + 2x - 24 = x² + 6x - 4x - 24 = x(x + 6) - 4(x + 6) = (x - 4)(x + 6)

We have same factor of x + 6:

• x + 6 = 0
• x = - 6 is a hole