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Note that the least common denominator (lcd) of 3 and 5 is 15.
[tex]\begin{aligned} & \frac{x}{3} + \frac{2x}{5} \\ & \frac{x(5) + 2x(3)}{3(5)} \\ & \frac{5x + 6x}{15} \\ & \boxed{\frac{11x}{15}} \end{aligned}[/tex]
Hence, the simplest form is [tex]\bold{\frac{11x}{15}}[/tex].
[tex]\large\bold{SOLUTION}[/tex]
[tex]\frac{x}{3}+\frac{2x}{5}[/tex]
Find the lcd ( lcd of 3 and 5 is 15)
[tex]\frac{x}{3}+\frac{2x}{5}=\frac{a}{15}+\frac{b}{15}[/tex]
Let a and b be unknown variables. To determine its equivalent numerator, divide the lcd to the denominator and multiply to the numerator.
[tex]a=(\frac{15}{3})(x)=5x[/tex]
[tex]b=(\frac{15}{5})(2x)=6x[/tex]
[tex]\frac{x}{3}+\frac{2x}{5}=\frac{5x}{15}+\frac{6x}{15}[/tex]
Simplify
[tex]\frac{5x}{15}+\frac{6x}{15}=\frac{11x}{15}[/tex]