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