What is true about the solution above.

Question

asked Jul 28, 2020 96.8k views

1 Answer

DerApe · Answer 1 · 2020-08-04T12:11:37+0000

ANSWER

$x = \pm √(3)$

and they are actual solutions.

Step-by-step explanation

The given equation is:

$\frac{ {x}^(2) }{2x - 6} = (9)/(6x - 18)$

Cross multiply

${x}^(2) (6x - 18) = 9(2x -6 )$

This implies;

${x}^(2) (6x - 18) - 9(2x - 6) = 0$

$3{x}^(2) (2x - 6) - 9(2x - 6) = 0$

Factor

$(3 {x}^(2) - 9)(2x - 6) = 0$

$3 {x}^(2) - 9 = 0 \: or \: 2x - 6= 0$

$3 {x}^(2) = 9 \: or \: 2x = 6$

${x}^(2) = 3\: or \: x = 3$

${x} = \pm √(3) \: or \: x = 3$

The domain of the given equation is

$x \\e3$

Therefore the actual solutions are

$x = \pm √(3)$

NB: x=3 is not in the domain of the given equation. It cannot be an extraneous solution.