state the excluded values for the following expression then

state the excluded values for the following expression. then simplify the expression.

state the excluded values for the following expression. then simplify the expression. frac{x^{2}-36}{x^{2}+15x+54}

(x² - 36)/(x² + 15x + 54)

The function is undefined when the denominator is equal to zero

==> x² + 15x + 54 = 0

==> x² + 6x + 9x + 54 = 0

==> x(x + 6) + 9(x + 6) = 0

==> (x + 6)(x + 9) = 0

==> x = -6 , -9

Hence excluded values are x = -6 , -9

(x² - 36)/(x² + 15x + 54) = (x² - 6²)/[(x + 6)(x + 9)]

==> (x - 6)(x + 6) / [(x + 6)(x + 9)] ; since (a - b)(a + b) = a² - b²

==> (x - 6)/(x + 9)

Hence simplified expression of (x² - 36)/(x² + 15x + 54) is (x - 6)/(x + 9)