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\frac{y}{x\left(x-y\right)}+\frac{x+y}{3\left(x-y\right)}
Factor x^{2}-xy. Factor 3x-3y.
\frac{3y}{3x\left(x-y\right)}+\frac{\left(x+y\right)x}{3x\left(x-y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x-y\right) and 3\left(x-y\right) is 3x\left(x-y\right). Multiply \frac{y}{x\left(x-y\right)} times \frac{3}{3}. Multiply \frac{x+y}{3\left(x-y\right)} times \frac{x}{x}.
\frac{3y+\left(x+y\right)x}{3x\left(x-y\right)}
Since \frac{3y}{3x\left(x-y\right)} and \frac{\left(x+y\right)x}{3x\left(x-y\right)} have the same denominator, add them by adding their numerators.
\frac{3y+x^{2}+yx}{3x\left(x-y\right)}
Do the multiplications in 3y+\left(x+y\right)x.
\frac{3y+x^{2}+yx}{3x^{2}-3xy}
Expand 3x\left(x-y\right).
\frac{y}{x\left(x-y\right)}+\frac{x+y}{3\left(x-y\right)}
Factor x^{2}-xy. Factor 3x-3y.
\frac{3y}{3x\left(x-y\right)}+\frac{\left(x+y\right)x}{3x\left(x-y\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x-y\right) and 3\left(x-y\right) is 3x\left(x-y\right). Multiply \frac{y}{x\left(x-y\right)} times \frac{3}{3}. Multiply \frac{x+y}{3\left(x-y\right)} times \frac{x}{x}.
\frac{3y+\left(x+y\right)x}{3x\left(x-y\right)}
Since \frac{3y}{3x\left(x-y\right)} and \frac{\left(x+y\right)x}{3x\left(x-y\right)} have the same denominator, add them by adding their numerators.
\frac{3y+x^{2}+yx}{3x\left(x-y\right)}
Do the multiplications in 3y+\left(x+y\right)x.
\frac{3y+x^{2}+yx}{3x^{2}-3xy}
Expand 3x\left(x-y\right).