Which solution to the equation 1/(x - 1) = (x - 2) / (2x² - 2) is extraneous
x = 1 and x = -4
Neither x = 1 or x = -4
x = 1
x = -4

Solution:

When the solution to an equation does not fit back into the equation, the solution is said to be an extraneous solution.

Let us solve the equation using and then check if it is an extraneous solution.

Step 1: Simplify the equation by cross multiplication.

 (2x² - 2) = (x - 1) (x - 2)

Step 2: Solve the equation to get the solution.

2x² - 2 = x² - 3x + 2

x² + 3x - 4 = 0

Step 3: Factorize the quadratic equation by splitting the middle term.

x² + 4x - x - 4 = 0

x(x + 4) - 1(x + 4) = 0

(x - 1)(x + 4) = 0

x = 1 or x = -4

Step 4: Substitute the values of x in the equation and check whether it satisfies the equation or not.

Check x = 1

1/(1 - 1) = (1 - 2)/(2(1)² - 2)

1/ 0 = 1/ 0

Since a rational number can not have 0 as a denominator, x= 1 is an extraneous solution.

Check x = -4

1/(-4 - 1) = (-4 - 2) / (2(-4)² - 2)

1/ -5 = - 6/30

- 1/5 = - 1/5

x = -4 satisfies the equation. Therefore x= 1 is the extraneous solution.

Which solution to the equation 1/(x - 1) = (x - 2) / (2x² - 2) is extraneous x = 1 and x = - 4, neither x = 1 or x = - 4, x = 1, x = - 4

Summary:

x = 1 is an extraneous solution for the equation 1/(x - 1) = (x - 2)/(2x² - 2).