Solve for x and simplify the answer fully. \[ \frac{x+3}{x-1}=\frac{5}{9} \]

Solve the equation \( \frac{x+3}{x-1}=\frac{5}{9} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{x+3}{x-1}=\frac{5}{9}\) - step1: Find the domain: \(\frac{x+3}{x-1}=\frac{5}{9},x\neq 1\) - step2: Cross multiply: \(\left(x+3\right)\times 9=\left(x-1\right)\times 5\) - step3: Simplify the equation: \(9\left(x+3\right)=5\left(x-1\right)\) - step4: Calculate: \(9x+27=5\left(x-1\right)\) - step5: Calculate: \(9x+27=5x-5\) - step6: Move the expression to the left side: \(9x+27-\left(5x-5\right)=0\) - step7: Calculate: \(4x+32=0\) - step8: Move the constant to the right side: \(4x=0-32\) - step9: Remove 0: \(4x=-32\) - step10: Divide both sides: \(\frac{4x}{4}=\frac{-32}{4}\) - step11: Divide the numbers: \(x=-8\) - step12: Check if the solution is in the defined range: \(x=-8,x\neq 1\) - step13: Find the intersection: \(x=-8\) The solution to the equation \(\frac{x+3}{x-1}=\frac{5}{9}\) is \(x=-8\).