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

Step-by-step explanation:

The given equation: $\dfrac{6}{x^2-9}-\dfrac{1}{x-3}=1$

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

$\dfrac{6}{(x-3)(x+3)}-\dfrac{1}{x-3}=1\\\\\Rightarrow\ \dfrac{6-(x+3)}{(x-3)(x+3)}=1\\\\\Rightarrow\ \dfrac{6-x-3}{(x-3)(x+3)}=1\\\\\Rightarrow\ 3-x=(x-3)(x+3)\\\\\Rightarrow\ (-1)(x-3)=(x-3)(x+3)\\\\\Rightarrow\ -1=x+3\\\\\Rightarrow\ x=-1-3=-4 \ \ \ [x\neq3]$

Hence, the solution is : x=-4

The correct option is B.