Question

Which solution to the equation StartFraction 1 Over x minus 1 EndFraction = StartFraction x minus 2 Over 2 x squared minus 2 EndFraction is extraneous? x = 1 and x = –4 neither x = 1 or x = –4 x = 1 x = –4

Answer 1

Answer:

x=1

Step-by-step explanation:

Answer 2

Answer:

x = - 4

Step-by-step explanation:

Given the expression

$\frac{1}{x-1} = \frac{x-2}{2x^2-2}$

This can also be expressed as;

$\frac{1}{x-1} = \frac{x-2}{2(x-1)(x+1)}\\1 = \frac{x-2}{2(x+1)}$

Cross multiply

$2(x+1) = x - 2\\2x+2 = x-2$

Add 2 to both sides

$2x+2+2 = x-2+2\\2x+4 = x\\2x-x = -4\\x = -4$

Hence the required extraneous solution is x = -4