Solve 6/ x - 4 = 4/ x for x and determine if the solution is extraneous or not.

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 algebra:

Given 6/ (x - 4) = 4/ x be eq (1).

Step 1: Simplify the equation by cross multiplication.

6x = 4 (x - 4) be equation (2)

Step 2: Solve the equation to get the solution.

6 x = 4x - 16

Step 3: Subtract both sides by 4x

6x - 4x = 4x - 16 - 4x

2x = - 16

Step 4: Divide both sides by 2.(using division property of equality)

2x/ 2 = - 16/ 2

x = - 8

Check x = - 8 using equation (2).

6(- 8) = 4 (- 8 - 4)

- 48 = 4 (- 12)

- 48 = - 48

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Solve 6/ x - 4 = 4/ x for x and determine if the solution is extraneous or not.

Summary:

x = - 8 is a non - extraneous solution for the equation 6/ (x - 4) = 4/ x.