Which of the options below give the solution to the equation ​$$\frac{1}{x+3} + \frac{1}{x+5} = \frac{1}{6}$$ ?​​

Correct option is A

Given : 

$$\frac{1}{x+3} + \frac{1}{x+5} = \frac{1}{6}$$

Formula Used: 

For quadratic equation  $$ax^2+bx+c=0$$​

quadratic formula =  $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$​​

Solution : 

$$\frac{1}{x+3} + \frac{1}{x+5}$$

$$=\frac{(x+5) + (x+3)}{(x+3)(x+5)}$$

$$=\frac{2x+8}{(x+3)(x+5)}$$

​​​​$$=\frac{2x+8}{(x+3)(x+5)} = \frac{1}{6}$$

= 6 (2x+8) = (x+3) (x+5)

​$$=12x + 48 = x^2 + 8x + 15$$

$$=x^2 - 4x - 33 = 0$$

​$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

​$$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-33)}}{2(1)}$$

$$x = \frac{4 \pm \sqrt{16 + 132}}{2}$$

$$x = \frac{4 \pm \sqrt{148}}{2}$$

$$x = \frac{4 \pm 2\sqrt{37}}{2}$$

$$x = 2 \pm \sqrt{37}$$​​​​​​​​

​​