Question

Select all of the domain values that would result in a denominator of zero for the equation
x/x-2 + 1/x-6 = 4/x^2-8x+12

Answer 1

Answer:

Options (4) and (5)

Step-by-step explanation:

Given equation is,

$\frac{x}{x-2}+\frac{1}{x-6}=\frac{4}{x^2-8x+12}$

$\frac{x(x-6)+(x-2)}{(x-2)(x-6)}=\frac{4}{x^2-8x+12}$

$\frac{x^2-5x-2}{(x-2)(x-6)}=\frac{4}{x^2-6x-2x+12}$

$\frac{x^2-5x-2}{(x-2)(x-6)}=\frac{4}{x(x-6)-2(x-6)}$

$\frac{x^2-5x-2}{(x-2)(x-6)}=\frac{4}{(x-2)(x-6)}$

$\frac{x^2-5x-2}{(x-2)(x-6)}-\frac{4}{(x-2)(x-6)}=0$

$\frac{x^2-5x-6}{(x-2)(x-6)}=0$

Therefore, domain values that will result in a denominator of zero for the equation will be,

(x - 2) = 0 ⇒ x = 2

(x - 6) = 0 ⇒ x = 6

Therefore, options (4) and (5) will be the correct options.