Evaluate
\frac{40n}{27m\left(a+3\right)}
Expand
\frac{40n}{27m\left(a+3\right)}
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\frac{\left(8a-24\right)\times 5mn^{2}}{9m^{2}n\left(3a^{2}-27\right)}
Divide \frac{8a-24}{9m^{2}n} by \frac{3a^{2}-27}{5mn^{2}} by multiplying \frac{8a-24}{9m^{2}n} by the reciprocal of \frac{3a^{2}-27}{5mn^{2}}.
\frac{5n\left(8a-24\right)}{9m\left(3a^{2}-27\right)}
Cancel out mn in both numerator and denominator.
\frac{5\times 8n\left(a-3\right)}{3\times 9m\left(a-3\right)\left(a+3\right)}
Factor the expressions that are not already factored.
\frac{5\times 8n}{3\times 9m\left(a+3\right)}
Cancel out a-3 in both numerator and denominator.
\frac{40n}{27am+81m}
Expand the expression.
\frac{\left(8a-24\right)\times 5mn^{2}}{9m^{2}n\left(3a^{2}-27\right)}
Divide \frac{8a-24}{9m^{2}n} by \frac{3a^{2}-27}{5mn^{2}} by multiplying \frac{8a-24}{9m^{2}n} by the reciprocal of \frac{3a^{2}-27}{5mn^{2}}.
\frac{5n\left(8a-24\right)}{9m\left(3a^{2}-27\right)}
Cancel out mn in both numerator and denominator.
\frac{5\times 8n\left(a-3\right)}{3\times 9m\left(a-3\right)\left(a+3\right)}
Factor the expressions that are not already factored.
\frac{5\times 8n}{3\times 9m\left(a+3\right)}
Cancel out a-3 in both numerator and denominator.
\frac{40n}{27am+81m}
Expand the expression.
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\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}