from sympy import symbols, Eq, solve

# Define the variable
x = symbols('x')

# Equation 13: Solve the equation (9x + 2)/(x - 9) = 2/5
equation_13 = Eq((9*x + 2)/(x - 9), 2/5)

# Solve for x
solution_13 = solve(equation_13, x)

# Problem 14: Simplify the expression (9x^4 / 16y^3) * (20y^2 / 81x^4)
y = symbols('y')

# Simplify the expression
numerator_14 = 9 * 20 * x**4 * y**2
denominator_14 = 16 * 81 * y**3 * x**4

# Simplify the expression
simplified_expression_14 = numerator_14 / denominator_14
simplified_expression_14 = simplified_expression_14.simplify()

solution_13, simplified_expression_14The solutions are:

1. **Problem 13:** The exact solution for the equation is \( x = -\frac{28}{43} \) or approximately \( x = -0.651 \).

2. **Problem 14:** The simplified expression is \( \frac{5}{36y} \).

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Explore detailed solutions for solving equations and simplifying algebraic expressions. Includes solving the equation (9x + 2)/(x - 9) = 2/5 and simplifying the expression (9x^4 / 16y^3) * (20y^2 / 81x^4). Suitable for advanced high school students and those interested in algebraic problem-solving.

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