Question

Evaluate
xy^{-2}+\frac{x}{y}\ x=-2y=\frac{1}{2}

Answer 1

To evaluate the expression \( xy^{-2} + \frac{x}{y} \) given the values \( x = -2 \) and \( y = \frac{1}{2} \), we first substitute these values into the expression.

1. **Substituting the values:**
\[
x = -2, \quad y = \frac{1}{2}
\]

2. **Calculating \( y^{-2} \):**
\[
y^{-2} = \left(\frac{1}{2}\right)^{-2} = 2^2 = 4
\]

3. **Calculating \( xy^{-2} \):**
\[
xy^{-2} = (-2)(4) = -8
\]

4. **Calculating \( \frac{x}{y} \):**
\[
\frac{x}{y} = \frac{-2}{\frac{1}{2}} = -2 \times 2 = -4
\]

5. **Adding the two results:**
\[
xy^{-2} + \frac{x}{y} = -8 + (-4) = -8 - 4 = -12
\]

Thus, the value of the expression \( xy^{-2} + \frac{x}{y} \) is \(\boxed{-12}\).