Evaluate
\frac{17x}{15}+\frac{11}{10}
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\frac{17x}{15}+\frac{11}{10}
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\frac{2}{3}\times \frac{1}{2}x+\frac{2}{3}\left(-\frac{3}{4}\right)+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Use the distributive property to multiply \frac{2}{3} by \frac{1}{2}x-\frac{3}{4}.
\frac{2\times 1}{3\times 2}x+\frac{2}{3}\left(-\frac{3}{4}\right)+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Multiply \frac{2}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{3}x+\frac{2}{3}\left(-\frac{3}{4}\right)+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Cancel out 2 in both numerator and denominator.
\frac{1}{3}x+\frac{2\left(-3\right)}{3\times 4}+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Multiply \frac{2}{3} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{3}x+\frac{-6}{12}+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Do the multiplications in the fraction \frac{2\left(-3\right)}{3\times 4}.
\frac{1}{3}x-\frac{1}{2}+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.
\frac{1}{3}x-\frac{1}{2}+\frac{2}{5}\left(2x+4\right)
Divide 10 by 5 to get 2.
\frac{1}{3}x-\frac{1}{2}+\frac{2}{5}\times 2x+\frac{2}{5}\times 4
Use the distributive property to multiply \frac{2}{5} by 2x+4.
\frac{1}{3}x-\frac{1}{2}+\frac{2\times 2}{5}x+\frac{2}{5}\times 4
Express \frac{2}{5}\times 2 as a single fraction.
\frac{1}{3}x-\frac{1}{2}+\frac{4}{5}x+\frac{2}{5}\times 4
Multiply 2 and 2 to get 4.
\frac{1}{3}x-\frac{1}{2}+\frac{4}{5}x+\frac{2\times 4}{5}
Express \frac{2}{5}\times 4 as a single fraction.
\frac{1}{3}x-\frac{1}{2}+\frac{4}{5}x+\frac{8}{5}
Multiply 2 and 4 to get 8.
\frac{17}{15}x-\frac{1}{2}+\frac{8}{5}
Combine \frac{1}{3}x and \frac{4}{5}x to get \frac{17}{15}x.
\frac{17}{15}x-\frac{5}{10}+\frac{16}{10}
Least common multiple of 2 and 5 is 10. Convert -\frac{1}{2} and \frac{8}{5} to fractions with denominator 10.
\frac{17}{15}x+\frac{-5+16}{10}
Since -\frac{5}{10} and \frac{16}{10} have the same denominator, add them by adding their numerators.
\frac{17}{15}x+\frac{11}{10}
Add -5 and 16 to get 11.
\frac{2}{3}\times \frac{1}{2}x+\frac{2}{3}\left(-\frac{3}{4}\right)+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Use the distributive property to multiply \frac{2}{3} by \frac{1}{2}x-\frac{3}{4}.
\frac{2\times 1}{3\times 2}x+\frac{2}{3}\left(-\frac{3}{4}\right)+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Multiply \frac{2}{3} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{3}x+\frac{2}{3}\left(-\frac{3}{4}\right)+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Cancel out 2 in both numerator and denominator.
\frac{1}{3}x+\frac{2\left(-3\right)}{3\times 4}+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Multiply \frac{2}{3} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{3}x+\frac{-6}{12}+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Do the multiplications in the fraction \frac{2\left(-3\right)}{3\times 4}.
\frac{1}{3}x-\frac{1}{2}+\frac{2}{5}\left(\frac{10}{5}x+4\right)
Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.
\frac{1}{3}x-\frac{1}{2}+\frac{2}{5}\left(2x+4\right)
Divide 10 by 5 to get 2.
\frac{1}{3}x-\frac{1}{2}+\frac{2}{5}\times 2x+\frac{2}{5}\times 4
Use the distributive property to multiply \frac{2}{5} by 2x+4.
\frac{1}{3}x-\frac{1}{2}+\frac{2\times 2}{5}x+\frac{2}{5}\times 4
Express \frac{2}{5}\times 2 as a single fraction.
\frac{1}{3}x-\frac{1}{2}+\frac{4}{5}x+\frac{2}{5}\times 4
Multiply 2 and 2 to get 4.
\frac{1}{3}x-\frac{1}{2}+\frac{4}{5}x+\frac{2\times 4}{5}
Express \frac{2}{5}\times 4 as a single fraction.
\frac{1}{3}x-\frac{1}{2}+\frac{4}{5}x+\frac{8}{5}
Multiply 2 and 4 to get 8.
\frac{17}{15}x-\frac{1}{2}+\frac{8}{5}
Combine \frac{1}{3}x and \frac{4}{5}x to get \frac{17}{15}x.
\frac{17}{15}x-\frac{5}{10}+\frac{16}{10}
Least common multiple of 2 and 5 is 10. Convert -\frac{1}{2} and \frac{8}{5} to fractions with denominator 10.
\frac{17}{15}x+\frac{-5+16}{10}
Since -\frac{5}{10} and \frac{16}{10} have the same denominator, add them by adding their numerators.
\frac{17}{15}x+\frac{11}{10}
Add -5 and 16 to get 11.
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}