Evaluate
\frac{3x^{2}-6x-8}{\left(x-2\right)^{4}}
Expand
\frac{3x^{2}-6x-8}{\left(x-2\right)^{4}}
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\frac{1}{\left(x-2\right)^{2}}+\frac{\left(x-3\right)\left(2x+4\right)}{\left(x-2\right)^{4}}
Express \left(x-3\right)\times \frac{2x+4}{\left(x-2\right)^{4}} as a single fraction.
\frac{\left(x-2\right)^{2}}{\left(x-2\right)^{4}}+\frac{\left(x-3\right)\left(2x+4\right)}{\left(x-2\right)^{4}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)^{2} and \left(x-2\right)^{4} is \left(x-2\right)^{4}. Multiply \frac{1}{\left(x-2\right)^{2}} times \frac{\left(x-2\right)^{2}}{\left(x-2\right)^{2}}.
\frac{\left(x-2\right)^{2}+\left(x-3\right)\left(2x+4\right)}{\left(x-2\right)^{4}}
Since \frac{\left(x-2\right)^{2}}{\left(x-2\right)^{4}} and \frac{\left(x-3\right)\left(2x+4\right)}{\left(x-2\right)^{4}} have the same denominator, add them by adding their numerators.
\frac{x^{2}-4x+4+2x^{2}+4x-6x-12}{\left(x-2\right)^{4}}
Do the multiplications in \left(x-2\right)^{2}+\left(x-3\right)\left(2x+4\right).
\frac{3x^{2}-6x-8}{\left(x-2\right)^{4}}
Combine like terms in x^{2}-4x+4+2x^{2}+4x-6x-12.
\frac{3x^{2}-6x-8}{x^{4}-8x^{3}+24x^{2}-32x+16}
Expand \left(x-2\right)^{4}.
\frac{1}{\left(x-2\right)^{2}}+\frac{\left(x-3\right)\left(2x+4\right)}{\left(x-2\right)^{4}}
Express \left(x-3\right)\times \frac{2x+4}{\left(x-2\right)^{4}} as a single fraction.
\frac{\left(x-2\right)^{2}}{\left(x-2\right)^{4}}+\frac{\left(x-3\right)\left(2x+4\right)}{\left(x-2\right)^{4}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)^{2} and \left(x-2\right)^{4} is \left(x-2\right)^{4}. Multiply \frac{1}{\left(x-2\right)^{2}} times \frac{\left(x-2\right)^{2}}{\left(x-2\right)^{2}}.
\frac{\left(x-2\right)^{2}+\left(x-3\right)\left(2x+4\right)}{\left(x-2\right)^{4}}
Since \frac{\left(x-2\right)^{2}}{\left(x-2\right)^{4}} and \frac{\left(x-3\right)\left(2x+4\right)}{\left(x-2\right)^{4}} have the same denominator, add them by adding their numerators.
\frac{x^{2}-4x+4+2x^{2}+4x-6x-12}{\left(x-2\right)^{4}}
Do the multiplications in \left(x-2\right)^{2}+\left(x-3\right)\left(2x+4\right).
\frac{3x^{2}-6x-8}{\left(x-2\right)^{4}}
Combine like terms in x^{2}-4x+4+2x^{2}+4x-6x-12.
\frac{3x^{2}-6x-8}{x^{4}-8x^{3}+24x^{2}-32x+16}
Expand \left(x-2\right)^{4}.
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}