Please help me solve and find the excluded values for this problem. Also please show me the work for this problem I want to learn!F(h) = x^2-9/x^2-4x+3

division by zero is not defined. So, when the denominator is zero, f(x) is not defined.

x^2-4x+3 = (x-1)(x-3)

so, when x=1 or 3, you are trying to divide by zero. Those values are not part of the domain.

Note that x^2-9 = (x-3)(x+3)

So, for any value except x=3, f(x) = (x+3)/(x-1)

The graph available below should help you explore other properties of f(x).

http://www.wolframalpha.com/input/?i=%28x^2-9%29%2F%28x^2-4x%2B3%29

To solve the problem and find the excluded values, we need to determine the values of x that would make the expression undefined. This happens when there is a division by zero.

Given function:

F(h) = (x^2 - 9) / (x^2 - 4x + 3)

To find the excluded values, we need to identify the values of x that will make the denominator of the fraction equal to zero. This is because division by zero is undefined.

Step 1: Set the denominator equal to zero and solve for x.

x^2 - 4x + 3 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula.

Method 1: Factoring

The equation factors into:

(x - 1)(x - 3) = 0

Now, set each factor equal to zero:

x - 1 = 0 and x - 3 = 0

Solving these equations, we find:

x = 1 and x = 3

Method 2: Quadratic Formula

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the quadratic equation x^2 - 4x + 3 = 0:

a = 1, b = -4, and c = 3

Plugging these values into the formula, we get:

x = (-(-4) ± √((-4)^2 - 4(1)(3))) / (2(1))

Simplifying further:

x = (4 ± √(16 - 12)) / 2

x = (4 ± √4) / 2

x = (4 ± 2) / 2

Solving for x, we find:

x = 3 and x = 1

Step 2: Check the excluded values by substituting them back into the original function.

Now that we have found the values of x that make the denominator zero (excluded values), we should check if these values also make the function undefined by substituting them back into the original function.

For x = 1:

F(h) = (1^2 - 9) / (1^2 - 4(1) + 3)
= (-8) / (0)

The function is undefined when x = 1.

For x = 3:

F(h) = (3^2 - 9) / (3^2 - 4(3) + 3)
= (0) / (0)

The function is undefined when x = 3.

So, the excluded values for this function are x = 1 and x = 3.

To summarize:
The excluded values for the given function F(h) = (x^2 - 9) / (x^2 - 4x + 3) are x = 1 and x = 3.