To solve the given expression, we need to find a common denominator and then combine the fractions. The given expression is:

\[
\frac{1}{y^2 - xy} + \frac{1}{x^2 - xy}
\]

First, let's factor the denominators:

\[
y^2 - xy = y(y - x)
\]
\[
x^2 - xy = x(x - y)
\]

Notice that \( x - y = -(y - x) \). So, the denominators can be rewritten as:

\[
y(y - x) \quad \text{and} \quad x(-(y - x)) = -x(y - x)
\]

Thus, the expression becomes:

\[
\frac{1}{y(y - x)} + \frac{1}{-x(y - x)}
\]

To combine these fractions, we need a common denominator. The common denominator is \( -xy(y - x) \):

\[
\frac{1}{y(y - x)} = \frac{1 \cdot (-x)}{y(y - x) \cdot (-x)} = \frac{-x}{-xy(y - x)}
\]
\[
\frac{1}{-x(y - x)} = \frac{1 \cdot y}{-x(y - x) \cdot y} = \frac{y}{-xy(y - x)}
\]

Now, we can combine the fractions:

\[
\frac{-x}{-xy(y - x)} + \frac{y}{-xy(y - x)} = \frac{-x + y}{-xy(y - x)}
\]

Simplify the numerator:

\[
\frac{y - x}{-xy(y - x)}
\]

Since \( y - x \) is a common factor in the numerator and the denominator, they cancel out:

\[
\frac{1}{-xy} = -\frac{1}{xy}
\]

So, the simplified form of the given expression is:

\[
-\frac{1}{xy}
\]