Respuesta :

The expression is [tex] \displaystyle{\frac{x^2-9x}{x^2-7x-18} [/tex].

The excluded values are those values of x for which the denominator, [tex]x^2-7x-18[/tex], becomes zero.

So, we need to factorize the expression [tex]x^2-7x-18[/tex].


To factorize the expression, we can use the grouping method. Write -7x as -9x+2x to create 4 terms, as follows:

                          [tex]x^2-7x-18=(x^2-9x)+(2x-18)=x(x-9)+2(x-9)[/tex].

The, factorizing (x-9), we have (x-9)(x+2).

This expression becomes 0 for x=-2, or for x=9.


Answer: {-2, 9}
MrRoyal

The excluded values of x for x^2-9x/x^2-7x-18 are -2 and 9

The expression is given as:

x^2-9x/x^2-7x-18

Set the denominator of the expression to 0

x^2-7x-18 = 0

Expand the above expression

x^2 + 2x -9x -18 = 0

Factorize the expression

x(x + 2) -9(x +2) = 0

Factor out x + 2

(x -9)(x +2) = 0

Solve for x

x = 9 and x = -2

Hence, the excluded values of x for x^2-9x/x^2-7x-18 are -2 and 9

Read more about quadratic functions at:

https://brainly.com/question/1214333

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