Evaluate
\frac{4\left(x+1\right)x^{2}\left(9x^{2}-6x+4\right)}{\left(3x-2\right)\left(27x^{4}+8\right)}
Expand
\frac{4\left(9x^{5}+3x^{4}-2x^{3}+4x^{2}\right)}{\left(3x-2\right)\left(27x^{4}+8\right)}
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\frac{4\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(3x-2\right)}\times \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8}
Factor the expressions that are not already factored in \frac{4x^{2}-4}{3x^{2}-5x+2}.
\frac{4\left(x+1\right)}{3x-2}\times \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8}
Cancel out x-1 in both numerator and denominator.
\frac{4\left(x+1\right)\left(9x^{4}-6x^{3}+4x^{2}\right)}{\left(3x-2\right)\left(27x^{4}+8\right)}
Multiply \frac{4\left(x+1\right)}{3x-2} times \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(4x+4\right)\left(9x^{4}-6x^{3}+4x^{2}\right)}{\left(3x-2\right)\left(27x^{4}+8\right)}
Use the distributive property to multiply 4 by x+1.
\frac{36x^{5}+12x^{4}-8x^{3}+16x^{2}}{\left(3x-2\right)\left(27x^{4}+8\right)}
Use the distributive property to multiply 4x+4 by 9x^{4}-6x^{3}+4x^{2} and combine like terms.
\frac{36x^{5}+12x^{4}-8x^{3}+16x^{2}}{81x^{5}+24x-54x^{4}-16}
Use the distributive property to multiply 3x-2 by 27x^{4}+8.
\frac{4\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(3x-2\right)}\times \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8}
Factor the expressions that are not already factored in \frac{4x^{2}-4}{3x^{2}-5x+2}.
\frac{4\left(x+1\right)}{3x-2}\times \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8}
Cancel out x-1 in both numerator and denominator.
\frac{4\left(x+1\right)\left(9x^{4}-6x^{3}+4x^{2}\right)}{\left(3x-2\right)\left(27x^{4}+8\right)}
Multiply \frac{4\left(x+1\right)}{3x-2} times \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(4x+4\right)\left(9x^{4}-6x^{3}+4x^{2}\right)}{\left(3x-2\right)\left(27x^{4}+8\right)}
Use the distributive property to multiply 4 by x+1.
\frac{36x^{5}+12x^{4}-8x^{3}+16x^{2}}{\left(3x-2\right)\left(27x^{4}+8\right)}
Use the distributive property to multiply 4x+4 by 9x^{4}-6x^{3}+4x^{2} and combine like terms.
\frac{36x^{5}+12x^{4}-8x^{3}+16x^{2}}{81x^{5}+24x-54x^{4}-16}
Use the distributive property to multiply 3x-2 by 27x^{4}+8.
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}