1. We are asked to express the expression $$\frac{y^2}{y^2 - x^2} - \frac{y}{y - x}$$ as a single simplified fraction. 2. Start by recognizing that the denominator $$y^2 - x^2$$ is a difference of squares, which factors as: $$ y^2 - x^2 = (y - x)(y + x) $$ 3. Rewrite the expression with this factorization: $$ \frac{y^2}{(y - x)(y + x)} - \frac{y}{y - x} $$ 4. To combine the fractions, find a common denominator. The second fraction lacks the factor $$y + x$$ in the denominator, so multiply numerator and denominator by $$y + x$$: $$ \frac{y^2}{(y - x)(y + x)} - \frac{y(y + x)}{(y - x)(y + x)} $$ 5. Now that both fractions have denominator $$ (y - x)(y + x) $$, combine the numerators: $$ \frac{y^2 - y(y + x)}{(y - x)(y + x)} $$ 6. Simplify the numerator: $$ y^2 - y(y + x) = y^2 - y^2 - yx = -yx $$ 7. So the expression becomes: $$ \frac{-yx}{(y - x)(y + x)} $$ 8. Therefore, the simplified single fraction is: $$ -\frac{yx}{(y - x)(y + x)} $$