Question

1. for which values of x is the expression undefined?\\(\frac{x^2 - 16}{9x - 45}\\)

Explanation:

Step1: Recall when a 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 value of \(x\) that makes the denominator \(9x - 45 = 0\).

Step2: Solve the equation for the denominator

Set the denominator equal to zero: \(9x - 45 = 0\).
Add 45 to both sides: \(9x = 45\).
Divide both sides by 9: \(x=\frac{45}{9}=5\).

Answer:

The expression is undefined when \(x = 5\).