Question

1. for which values of x is the expression undefined? \\(\frac{x^2 - 49}{x^2 + 2x - 24}\\)

Explanation:

Step1: Recall when rational expression is undefined

A rational expression \(\frac{f(x)}{g(x)}\) is undefined when the denominator \(g(x) = 0\). So we need to find the values of \(x\) that make the denominator \(x^{2}+2x - 24=0\).

Step2: Factor the quadratic equation

Factor the quadratic expression \(x^{2}+2x - 24\). We need two numbers that multiply to \(- 24\) and add up to \(2\). The numbers are \(6\) and \(-4\) because \(6\times(-4)=-24\) and \(6 + (-4)=2\). So, \(x^{2}+2x - 24=(x + 6)(x - 4)\).

Step3: Solve for x when denominator is zero

Set each factor equal to zero:

• For \(x + 6=0\), we get \(x=-6\).
• For \(x - 4=0\), we get \(x = 4\).

Answer:

The expression is undefined when \(x = 4\) and \(x=-6\)