Question

What is the solution to the rational equation x over x squared minus 9 minus 1 over x plus 3 equals 1 over 4x minus 12

Answer 1

The LCD is 4(x^2 - 9)
Multiplying each term by the LCD:-

4x - 4(x - 3) = x + 3
12 = x + 3

x = 9 answer

Answer 2

The correct answer is the last option x=9

Explanation:

Step 1

First step is to factor out the denominators. This step is shown below,

`(x)/(x^2-9) -(1)/(x+3) =(1)/(4x-12)\\(x)/((x+3)(x-3)) -(1)/(x+3)=(1)/(4(x-3))`

Step 2

The next step is to multiply both sides of the equation by
`4(x-3)(x+3)` and solve for x.

This process is shown below,

`4(x+3)(x-3)\bigl[ (x)/((x+3)(x-3)) -(1)/((x+3)) \bigr]=4(x+3)(x-3)\bigl[(1)/(4(x-3)) \bigr]\\\implies 4x-4(x-3)=(x+3)\\\implies 4x-4x+12=x+3\\\implies 12=x+3\\\implies 12-3=x\\\implies 9=x`

The answer is
`x=9.`