Solve for x: 5 over x plus 8 equals 3 over x and determine if the solution is extraneous or not?

The given expression 5 over x plus 8 equals 3 over x represents a monomial.

Answer: x = 12, and the solution is not extraneous for 5 over x plus 8 equals 3 over x for x.

Let us solve it step by step.

Explanation:

Given: 5 over x plus 8 equals 3 over x

The mathematical equation for the statement is: 5 / (x+8) = 3 / x

On solving the equation for the value of x, we get:

Cross-multiplying 5 / (x+8) = 3 / x:

5x = 3(x + 8)

5x = 3x + 24

2x = 24

x = 12

Now we have to check whether the solution is extraneous or not.

If the value of x does not satisfy the given equation, the solution is extraneous.

If the value of x satisfies the equation, the solution is not extraneous or it is a verified solution.

Let's check it for x =12,

Substitute x = 12

5 / (12 + 8) = 3 / 12

1 / 4 = 1 / 4

No undefined values occurred, so x = 12 is non-extraneous.

Therefore, x = 12, and the solution is not extraneous for 5 over x plus 8 equals 3 over x for x.