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\frac{13a-30b}{10ab}
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\frac{13a-30b}{10ab}
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\frac{13}{10b}-\frac{5+10}{5a}
Add 4 and 9 to get 13.
\frac{13}{10b}-\frac{15}{5a}
Add 5 and 10 to get 15.
\frac{13a}{10ab}-\frac{15\times 2b}{10ab}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10b and 5a is 10ab. Multiply \frac{13}{10b} times \frac{a}{a}. Multiply \frac{15}{5a} times \frac{2b}{2b}.
\frac{13a-15\times 2b}{10ab}
Since \frac{13a}{10ab} and \frac{15\times 2b}{10ab} have the same denominator, subtract them by subtracting their numerators.
\frac{13a-30b}{10ab}
Do the multiplications in 13a-15\times 2b.
\frac{13}{10b}-\frac{5+10}{5a}
Add 4 and 9 to get 13.
\frac{13}{10b}-\frac{15}{5a}
Add 5 and 10 to get 15.
\frac{13a}{10ab}-\frac{15\times 2b}{10ab}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10b and 5a is 10ab. Multiply \frac{13}{10b} times \frac{a}{a}. Multiply \frac{15}{5a} times \frac{2b}{2b}.
\frac{13a-15\times 2b}{10ab}
Since \frac{13a}{10ab} and \frac{15\times 2b}{10ab} have the same denominator, subtract them by subtracting their numerators.
\frac{13a-30b}{10ab}
Do the multiplications in 13a-15\times 2b.
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}