Question

What is this problem: It is also a rational function. 6 / x^2 - 9 - 1 / x - 3 = 1 Answers: A) -1+-sqr(73) / 2 B)-4 C)2 D)3 or -4

Answer 1

Answer: B)-4

Explanation:

The given equation:
`(6)/(x^2-9)-(1)/(x-3)=1`

Using identity:
`a^2-b^2=(a-b)(a+b)`

`(6)/((x-3)(x+3))-(1)/(x-3)=1\\\\\Rightarrow\ (6-(x+3))/((x-3)(x+3))=1\\\\\Rightarrow\ (6-x-3)/((x-3)(x+3))=1\\\\\Rightarrow\ 3-x=(x-3)(x+3)\\\\\Rightarrow\ (-1)(x-3)=(x-3)(x+3)\\\\\Rightarrow\ -1=x+3\\\\\Rightarrow\ x=-1-3=-4 \ \ \ [x\\eq3]`

Hence, the solution is : x=-4

The correct option is B.