What are the excluded values of x for x^2-9x/x^2-7x-18

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}