If \frac{x}{8} - \frac{2}{x} = 0 and x > 0, what is the value of x? — SAT

If $\frac{x}{8} - \frac{2}{x} = 0$ and $x > 0$ , what is the value of $x$ ?

Answer: 4

The correct answer is 4. Adding the term

\frac{2}{x}

to both sides of the equation yields

\frac{x}{8} = \frac{2}{x}

. Cross-multiplying the terms gives

x^2 = 16

. Solving for

x

by taking the square root of both sides gives

x = 4

x = -4

. Since the question specifies that

x > 0

, the negative value is discarded, leaving 4 as the only valid solution.

Add

\frac{2}{x}

to both sides of the equation.

\frac{x}{8} = \frac{2}{x}

To isolate the rational terms on opposite sides of the equation.

Cross-multiply the terms.

x^2 = 16

To eliminate the denominators and form a quadratic equation.

Solve for

x

by taking the square root of both sides.

x = 4

x = -4

Taking the square root of 16 yields both positive and negative solutions.

Apply the constraint

x > 0

x = 4

The question specifies that

x

must be greater than 0, which excludes the negative solution.

Solving rational equations by isolating terms, cross-multiplying, and applying given constraints.

Question