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

Options (4) and (5)

Explanation:

Given equation is,

`(x)/(x-2)+(1)/(x-6)=(4)/(x^2-8x+12)`

`(x(x-6)+(x-2))/((x-2)(x-6))=(4)/(x^2-8x+12)`

`(x^2-5x-2)/((x-2)(x-6))=(4)/(x^2-6x-2x+12)`

`(x^2-5x-2)/((x-2)(x-6))=(4)/(x(x-6)-2(x-6))`

`(x^2-5x-2)/((x-2)(x-6))=(4)/((x-2)(x-6))`

`(x^2-5x-2)/((x-2)(x-6))-(4)/((x-2)(x-6))=0`

`(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.