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\frac{19a+b}{15}
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\frac{19a+b}{15}
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\frac{3\left(3a+2b\right)}{15}-\frac{5\left(b-2a\right)}{15}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3 is 15. Multiply \frac{3a+2b}{5} times \frac{3}{3}. Multiply \frac{b-2a}{3} times \frac{5}{5}.
\frac{3\left(3a+2b\right)-5\left(b-2a\right)}{15}
Since \frac{3\left(3a+2b\right)}{15} and \frac{5\left(b-2a\right)}{15} have the same denominator, subtract them by subtracting their numerators.
\frac{9a+6b-5b+10a}{15}
Do the multiplications in 3\left(3a+2b\right)-5\left(b-2a\right).
\frac{19a+b}{15}
Combine like terms in 9a+6b-5b+10a.
\frac{3\left(3a+2b\right)}{15}-\frac{5\left(b-2a\right)}{15}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 3 is 15. Multiply \frac{3a+2b}{5} times \frac{3}{3}. Multiply \frac{b-2a}{3} times \frac{5}{5}.
\frac{3\left(3a+2b\right)-5\left(b-2a\right)}{15}
Since \frac{3\left(3a+2b\right)}{15} and \frac{5\left(b-2a\right)}{15} have the same denominator, subtract them by subtracting their numerators.
\frac{9a+6b-5b+10a}{15}
Do the multiplications in 3\left(3a+2b\right)-5\left(b-2a\right).
\frac{19a+b}{15}
Combine like terms in 9a+6b-5b+10a.
Examples
Quadratic equation
{ 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}