Question

Need help to find x. with the equation 9/x^2-9=3/6x-18

Answer 1

x = 15

Explanation:

Pre-Solving

We are given the following equation:

`(9)/(x^2-9) = (3)/(6x-18)`

We want to find the value of x of it.

Solving

Equation

We can start by cross multiplying to get:

9(6x-18) = 3(x²-9)

Distribute the 9 and 3.

54x - 162 = 3x² - 27

Subtract 54x from both sides

-162 = 3x² - 54x - 27

Add 162 to both sides.

3x² - 54x + 135 = 0

We can divide each term by 3. We'll end up with:

x² - 18x + 45 = 0

This can be factored to become:

(x -15)(x-3) = 0

Applying zero product property,

x - 15 = 0

x = 15

And:

x-3 = 0

x = 3

Domain

We aren't done yet though; we need to find the domain of this equation, because we have variables in the denominator.

x² - 9 and 6x - 18 both cannot be zero. Because of that:

x² - 9 ≠ 0

x² ≠ 9

x ≠ ±3

and:

6x - 18 ≠ 0

6x ≠ 18

x ≠ 3
The value of x cannot be 3 or -3. This means that our only answer is x = 15.