Evaluate
\frac{19x}{5}+\frac{1}{3}
Expand
\frac{19x}{5}+\frac{1}{3}
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3x\left(\frac{9}{15}+\frac{10}{15}\right)-\left(\frac{1}{3}-\frac{2}{3}\right)
Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{2}{3} to fractions with denominator 15.
3x\times \frac{9+10}{15}-\left(\frac{1}{3}-\frac{2}{3}\right)
Since \frac{9}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.
3x\times \frac{19}{15}-\left(\frac{1}{3}-\frac{2}{3}\right)
Add 9 and 10 to get 19.
\frac{3\times 19}{15}x-\left(\frac{1}{3}-\frac{2}{3}\right)
Express 3\times \frac{19}{15} as a single fraction.
\frac{57}{15}x-\left(\frac{1}{3}-\frac{2}{3}\right)
Multiply 3 and 19 to get 57.
\frac{19}{5}x-\left(\frac{1}{3}-\frac{2}{3}\right)
Reduce the fraction \frac{57}{15} to lowest terms by extracting and canceling out 3.
\frac{19}{5}x-\frac{1-2}{3}
Since \frac{1}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.
\frac{19}{5}x-\left(-\frac{1}{3}\right)
Subtract 2 from 1 to get -1.
\frac{19}{5}x+\frac{1}{3}
The opposite of -\frac{1}{3} is \frac{1}{3}.
3x\left(\frac{9}{15}+\frac{10}{15}\right)-\left(\frac{1}{3}-\frac{2}{3}\right)
Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{2}{3} to fractions with denominator 15.
3x\times \frac{9+10}{15}-\left(\frac{1}{3}-\frac{2}{3}\right)
Since \frac{9}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.
3x\times \frac{19}{15}-\left(\frac{1}{3}-\frac{2}{3}\right)
Add 9 and 10 to get 19.
\frac{3\times 19}{15}x-\left(\frac{1}{3}-\frac{2}{3}\right)
Express 3\times \frac{19}{15} as a single fraction.
\frac{57}{15}x-\left(\frac{1}{3}-\frac{2}{3}\right)
Multiply 3 and 19 to get 57.
\frac{19}{5}x-\left(\frac{1}{3}-\frac{2}{3}\right)
Reduce the fraction \frac{57}{15} to lowest terms by extracting and canceling out 3.
\frac{19}{5}x-\frac{1-2}{3}
Since \frac{1}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.
\frac{19}{5}x-\left(-\frac{1}{3}\right)
Subtract 2 from 1 to get -1.
\frac{19}{5}x+\frac{1}{3}
The opposite of -\frac{1}{3} is \frac{1}{3}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}