Evaluate
\frac{2\left(x+3\right)}{9\left(x+2\right)}
Expand
\frac{2\left(x+3\right)}{9\left(x+2\right)}
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\frac{\frac{\left(x^{2}-1\right)\left(x^{2}+6x+9\right)}{\left(x^{2}+5x+6\right)\left(2x+2\right)}}{\frac{9x-9}{4}}
Multiply \frac{x^{2}-1}{x^{2}+5x+6} times \frac{x^{2}+6x+9}{2x+2} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x^{2}-1\right)\left(x^{2}+6x+9\right)\times 4}{\left(x^{2}+5x+6\right)\left(2x+2\right)\left(9x-9\right)}
Divide \frac{\left(x^{2}-1\right)\left(x^{2}+6x+9\right)}{\left(x^{2}+5x+6\right)\left(2x+2\right)} by \frac{9x-9}{4} by multiplying \frac{\left(x^{2}-1\right)\left(x^{2}+6x+9\right)}{\left(x^{2}+5x+6\right)\left(2x+2\right)} by the reciprocal of \frac{9x-9}{4}.
\frac{4\left(x-1\right)\left(x+1\right)\left(x+3\right)^{2}}{2\times 9\left(x-1\right)\left(x+1\right)\left(x+2\right)\left(x+3\right)}
Factor the expressions that are not already factored.
\frac{2\left(x+3\right)}{9\left(x+2\right)}
Cancel out 2\left(x-1\right)\left(x+1\right)\left(x+3\right) in both numerator and denominator.
\frac{2x+6}{9x+18}
Expand the expression.
\frac{\frac{\left(x^{2}-1\right)\left(x^{2}+6x+9\right)}{\left(x^{2}+5x+6\right)\left(2x+2\right)}}{\frac{9x-9}{4}}
Multiply \frac{x^{2}-1}{x^{2}+5x+6} times \frac{x^{2}+6x+9}{2x+2} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x^{2}-1\right)\left(x^{2}+6x+9\right)\times 4}{\left(x^{2}+5x+6\right)\left(2x+2\right)\left(9x-9\right)}
Divide \frac{\left(x^{2}-1\right)\left(x^{2}+6x+9\right)}{\left(x^{2}+5x+6\right)\left(2x+2\right)} by \frac{9x-9}{4} by multiplying \frac{\left(x^{2}-1\right)\left(x^{2}+6x+9\right)}{\left(x^{2}+5x+6\right)\left(2x+2\right)} by the reciprocal of \frac{9x-9}{4}.
\frac{4\left(x-1\right)\left(x+1\right)\left(x+3\right)^{2}}{2\times 9\left(x-1\right)\left(x+1\right)\left(x+2\right)\left(x+3\right)}
Factor the expressions that are not already factored.
\frac{2\left(x+3\right)}{9\left(x+2\right)}
Cancel out 2\left(x-1\right)\left(x+1\right)\left(x+3\right) in both numerator and denominator.
\frac{2x+6}{9x+18}
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}