39x3y/26x2y2

To simplify the expression \(\frac{39x^3y}{26x^2y^2}\), we can divide both the numerator and the denominator by their common factors.

1. Factor the coefficients: \(\frac{39}{26}\) can be simplified: \[ 39 \div 13 = 3 \] \[ 26 \div 13 = 2 \] So, \(\frac{39}{26} = \frac{3}{2}\).

2. Simplify the variables:

   • For \(x\): \(\frac{x^3}{x^2} = x^{3-2} = x^1 = x\)
   • For \(y\): \(\frac{y}{y^2} = \frac{1}{y^{2-1}} = \frac{1}{y} = y^{-1}\)

Putting it all together, we get: \[ \frac{39x^3y}{26x^2y^2} = \frac{3}{2} \cdot x \cdot y^{-1} = \frac{3x}{2y} \]

Thus, the simplified expression is: \[ \frac{3x}{2y} \]