Evaluate
\frac{5\left(a-2\right)}{2b-1}
Expand
\frac{5\left(a-2\right)}{2b-1}
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\frac{4\left(a+2\right)}{6\left(2b-1\right)}\times \frac{3a-6}{4b+2}\times \frac{5+10b}{a+2}
Factor the expressions that are not already factored in \frac{4a+8}{12b-6}.
\frac{2\left(a+2\right)}{3\left(2b-1\right)}\times \frac{3a-6}{4b+2}\times \frac{5+10b}{a+2}
Cancel out 2 in both numerator and denominator.
\frac{2\left(a+2\right)\left(3a-6\right)}{3\left(2b-1\right)\left(4b+2\right)}\times \frac{5+10b}{a+2}
Multiply \frac{2\left(a+2\right)}{3\left(2b-1\right)} times \frac{3a-6}{4b+2} by multiplying numerator times numerator and denominator times denominator.
\frac{2\left(a+2\right)\left(3a-6\right)\left(5+10b\right)}{3\left(2b-1\right)\left(4b+2\right)\left(a+2\right)}
Multiply \frac{2\left(a+2\right)\left(3a-6\right)}{3\left(2b-1\right)\left(4b+2\right)} times \frac{5+10b}{a+2} by multiplying numerator times numerator and denominator times denominator.
\frac{2\left(3a-6\right)\left(10b+5\right)}{3\left(2b-1\right)\left(4b+2\right)}
Cancel out a+2 in both numerator and denominator.
\frac{2\times 3\times 5\left(a-2\right)\left(2b+1\right)}{2\times 3\left(2b-1\right)\left(2b+1\right)}
Factor the expressions that are not already factored.
\frac{5\left(a-2\right)}{2b-1}
Cancel out 2\times 3\left(2b+1\right) in both numerator and denominator.
\frac{5a-10}{2b-1}
Expand the expression.
\frac{4\left(a+2\right)}{6\left(2b-1\right)}\times \frac{3a-6}{4b+2}\times \frac{5+10b}{a+2}
Factor the expressions that are not already factored in \frac{4a+8}{12b-6}.
\frac{2\left(a+2\right)}{3\left(2b-1\right)}\times \frac{3a-6}{4b+2}\times \frac{5+10b}{a+2}
Cancel out 2 in both numerator and denominator.
\frac{2\left(a+2\right)\left(3a-6\right)}{3\left(2b-1\right)\left(4b+2\right)}\times \frac{5+10b}{a+2}
Multiply \frac{2\left(a+2\right)}{3\left(2b-1\right)} times \frac{3a-6}{4b+2} by multiplying numerator times numerator and denominator times denominator.
\frac{2\left(a+2\right)\left(3a-6\right)\left(5+10b\right)}{3\left(2b-1\right)\left(4b+2\right)\left(a+2\right)}
Multiply \frac{2\left(a+2\right)\left(3a-6\right)}{3\left(2b-1\right)\left(4b+2\right)} times \frac{5+10b}{a+2} by multiplying numerator times numerator and denominator times denominator.
\frac{2\left(3a-6\right)\left(10b+5\right)}{3\left(2b-1\right)\left(4b+2\right)}
Cancel out a+2 in both numerator and denominator.
\frac{2\times 3\times 5\left(a-2\right)\left(2b+1\right)}{2\times 3\left(2b-1\right)\left(2b+1\right)}
Factor the expressions that are not already factored.
\frac{5\left(a-2\right)}{2b-1}
Cancel out 2\times 3\left(2b+1\right) in both numerator and denominator.
\frac{5a-10}{2b-1}
Expand the expression.
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}