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\frac{5x}{3}+\frac{3x^{2}}{3}
To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{3}{3}.
\frac{5x+3x^{2}}{3}
Since \frac{5x}{3} and \frac{3x^{2}}{3} have the same denominator, add them by adding their numerators.
\frac{5x+3x^{2}}{3}
Factor out \frac{1}{3}.
x\left(5+3x\right)
Consider 5x+3x^{2}. Factor out x.
\frac{x\left(3x+5\right)}{3}
Rewrite the complete factored expression.