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\frac{3y-5}{2\left(y-3\right)}+\frac{4y-2}{5\left(y-3\right)}
Factor 2y-6. Factor 5y-15.
\frac{5\left(3y-5\right)}{10\left(y-3\right)}+\frac{2\left(4y-2\right)}{10\left(y-3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(y-3\right) and 5\left(y-3\right) is 10\left(y-3\right). Multiply \frac{3y-5}{2\left(y-3\right)} times \frac{5}{5}. Multiply \frac{4y-2}{5\left(y-3\right)} times \frac{2}{2}.
\frac{5\left(3y-5\right)+2\left(4y-2\right)}{10\left(y-3\right)}
Since \frac{5\left(3y-5\right)}{10\left(y-3\right)} and \frac{2\left(4y-2\right)}{10\left(y-3\right)} have the same denominator, add them by adding their numerators.
\frac{15y-25+8y-4}{10\left(y-3\right)}
Do the multiplications in 5\left(3y-5\right)+2\left(4y-2\right).
\frac{23y-29}{10\left(y-3\right)}
Combine like terms in 15y-25+8y-4.
\frac{23y-29}{10y-30}
Expand 10\left(y-3\right).
\frac{3y-5}{2\left(y-3\right)}+\frac{4y-2}{5\left(y-3\right)}
Factor 2y-6. Factor 5y-15.
\frac{5\left(3y-5\right)}{10\left(y-3\right)}+\frac{2\left(4y-2\right)}{10\left(y-3\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(y-3\right) and 5\left(y-3\right) is 10\left(y-3\right). Multiply \frac{3y-5}{2\left(y-3\right)} times \frac{5}{5}. Multiply \frac{4y-2}{5\left(y-3\right)} times \frac{2}{2}.
\frac{5\left(3y-5\right)+2\left(4y-2\right)}{10\left(y-3\right)}
Since \frac{5\left(3y-5\right)}{10\left(y-3\right)} and \frac{2\left(4y-2\right)}{10\left(y-3\right)} have the same denominator, add them by adding their numerators.
\frac{15y-25+8y-4}{10\left(y-3\right)}
Do the multiplications in 5\left(3y-5\right)+2\left(4y-2\right).
\frac{23y-29}{10\left(y-3\right)}
Combine like terms in 15y-25+8y-4.
\frac{23y-29}{10y-30}
Expand 10\left(y-3\right).