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.
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.