Score: 50/90 Answered: \( 7 / 9 \) Question 8 Solve the equation \( \frac{x}{4 x-16}-4=\frac{1}{x-4} \) Does the equation have a solution?

Solve the equation \( \frac{x}{4x-16}-4=\frac{1}{x-4} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{x}{4x-16}-4=\frac{1}{x-4}\) - step1: Find the domain: \(\frac{x}{4x-16}-4=\frac{1}{x-4},x\neq 4\) - step2: Multiply both sides of the equation by LCD: \(\left(\frac{x}{4x-16}-4\right)\times 4\left(x-4\right)=\frac{1}{x-4}\times 4\left(x-4\right)\) - step3: Simplify the equation: \(-15x+64=4\) - step4: Move the constant to the right side: \(-15x=4-64\) - step5: Subtract the numbers: \(-15x=-60\) - step6: Change the signs: \(15x=60\) - step7: Divide both sides: \(\frac{15x}{15}=\frac{60}{15}\) - step8: Divide the numbers: \(x=4\) - step9: Check if the solution is in the defined range: \(x=4,x\neq 4\) - step10: Find the intersection: \(x \in \varnothing \) The equation \( \frac{x}{4x-16}-4=\frac{1}{x-4} \) does not have a solution.