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

x=1

Explanation:

Answer 2

x = - 4

Explanation:

Given the expression

`(1)/(x-1) = (x-2)/(2x^2-2)`

This can also be expressed as;

`(1)/(x-1) = (x-2)/(2(x-1)(x+1))\\1 = (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