Evaluate
\frac{x^{3}+x^{2}-20x+26}{2\left(x-1\right)\left(x-2\right)^{2}}
Expand
\frac{x^{3}+x^{2}-20x+26}{2\left(x-1\right)\left(x-2\right)^{2}}
Graph
Share
Copied to clipboard
\frac{x+5}{2\left(x-1\right)}-\frac{1}{\left(x-2\right)\left(x-1\right)}-\frac{1}{x^{2}-4x+4}
Factor 2x-2. Factor x^{2}-3x+2.
\frac{\left(x+5\right)\left(x-2\right)}{2\left(x-2\right)\left(x-1\right)}-\frac{2}{2\left(x-2\right)\left(x-1\right)}-\frac{1}{x^{2}-4x+4}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-1\right) and \left(x-2\right)\left(x-1\right) is 2\left(x-2\right)\left(x-1\right). Multiply \frac{x+5}{2\left(x-1\right)} times \frac{x-2}{x-2}. Multiply \frac{1}{\left(x-2\right)\left(x-1\right)} times \frac{2}{2}.
\frac{\left(x+5\right)\left(x-2\right)-2}{2\left(x-2\right)\left(x-1\right)}-\frac{1}{x^{2}-4x+4}
Since \frac{\left(x+5\right)\left(x-2\right)}{2\left(x-2\right)\left(x-1\right)} and \frac{2}{2\left(x-2\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-2x+5x-10-2}{2\left(x-2\right)\left(x-1\right)}-\frac{1}{x^{2}-4x+4}
Do the multiplications in \left(x+5\right)\left(x-2\right)-2.
\frac{x^{2}+3x-12}{2\left(x-2\right)\left(x-1\right)}-\frac{1}{x^{2}-4x+4}
Combine like terms in x^{2}-2x+5x-10-2.
\frac{x^{2}+3x-12}{2\left(x-2\right)\left(x-1\right)}-\frac{1}{\left(x-2\right)^{2}}
Factor x^{2}-4x+4.
\frac{\left(x^{2}+3x-12\right)\left(x-2\right)}{2\left(x-1\right)\left(x-2\right)^{2}}-\frac{2\left(x-1\right)}{2\left(x-1\right)\left(x-2\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-2\right)\left(x-1\right) and \left(x-2\right)^{2} is 2\left(x-1\right)\left(x-2\right)^{2}. Multiply \frac{x^{2}+3x-12}{2\left(x-2\right)\left(x-1\right)} times \frac{x-2}{x-2}. Multiply \frac{1}{\left(x-2\right)^{2}} times \frac{2\left(x-1\right)}{2\left(x-1\right)}.
\frac{\left(x^{2}+3x-12\right)\left(x-2\right)-2\left(x-1\right)}{2\left(x-1\right)\left(x-2\right)^{2}}
Since \frac{\left(x^{2}+3x-12\right)\left(x-2\right)}{2\left(x-1\right)\left(x-2\right)^{2}} and \frac{2\left(x-1\right)}{2\left(x-1\right)\left(x-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{3}-2x^{2}+3x^{2}-6x-12x+24-2x+2}{2\left(x-1\right)\left(x-2\right)^{2}}
Do the multiplications in \left(x^{2}+3x-12\right)\left(x-2\right)-2\left(x-1\right).
\frac{x^{3}+x^{2}-20x+26}{2\left(x-1\right)\left(x-2\right)^{2}}
Combine like terms in x^{3}-2x^{2}+3x^{2}-6x-12x+24-2x+2.
\frac{x^{3}+x^{2}-20x+26}{2x^{3}-10x^{2}+16x-8}
Expand 2\left(x-1\right)\left(x-2\right)^{2}.
\frac{x+5}{2\left(x-1\right)}-\frac{1}{\left(x-2\right)\left(x-1\right)}-\frac{1}{x^{2}-4x+4}
Factor 2x-2. Factor x^{2}-3x+2.
\frac{\left(x+5\right)\left(x-2\right)}{2\left(x-2\right)\left(x-1\right)}-\frac{2}{2\left(x-2\right)\left(x-1\right)}-\frac{1}{x^{2}-4x+4}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-1\right) and \left(x-2\right)\left(x-1\right) is 2\left(x-2\right)\left(x-1\right). Multiply \frac{x+5}{2\left(x-1\right)} times \frac{x-2}{x-2}. Multiply \frac{1}{\left(x-2\right)\left(x-1\right)} times \frac{2}{2}.
\frac{\left(x+5\right)\left(x-2\right)-2}{2\left(x-2\right)\left(x-1\right)}-\frac{1}{x^{2}-4x+4}
Since \frac{\left(x+5\right)\left(x-2\right)}{2\left(x-2\right)\left(x-1\right)} and \frac{2}{2\left(x-2\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-2x+5x-10-2}{2\left(x-2\right)\left(x-1\right)}-\frac{1}{x^{2}-4x+4}
Do the multiplications in \left(x+5\right)\left(x-2\right)-2.
\frac{x^{2}+3x-12}{2\left(x-2\right)\left(x-1\right)}-\frac{1}{x^{2}-4x+4}
Combine like terms in x^{2}-2x+5x-10-2.
\frac{x^{2}+3x-12}{2\left(x-2\right)\left(x-1\right)}-\frac{1}{\left(x-2\right)^{2}}
Factor x^{2}-4x+4.
\frac{\left(x^{2}+3x-12\right)\left(x-2\right)}{2\left(x-1\right)\left(x-2\right)^{2}}-\frac{2\left(x-1\right)}{2\left(x-1\right)\left(x-2\right)^{2}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x-2\right)\left(x-1\right) and \left(x-2\right)^{2} is 2\left(x-1\right)\left(x-2\right)^{2}. Multiply \frac{x^{2}+3x-12}{2\left(x-2\right)\left(x-1\right)} times \frac{x-2}{x-2}. Multiply \frac{1}{\left(x-2\right)^{2}} times \frac{2\left(x-1\right)}{2\left(x-1\right)}.
\frac{\left(x^{2}+3x-12\right)\left(x-2\right)-2\left(x-1\right)}{2\left(x-1\right)\left(x-2\right)^{2}}
Since \frac{\left(x^{2}+3x-12\right)\left(x-2\right)}{2\left(x-1\right)\left(x-2\right)^{2}} and \frac{2\left(x-1\right)}{2\left(x-1\right)\left(x-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{3}-2x^{2}+3x^{2}-6x-12x+24-2x+2}{2\left(x-1\right)\left(x-2\right)^{2}}
Do the multiplications in \left(x^{2}+3x-12\right)\left(x-2\right)-2\left(x-1\right).
\frac{x^{3}+x^{2}-20x+26}{2\left(x-1\right)\left(x-2\right)^{2}}
Combine like terms in x^{3}-2x^{2}+3x^{2}-6x-12x+24-2x+2.
\frac{x^{3}+x^{2}-20x+26}{2x^{3}-10x^{2}+16x-8}
Expand 2\left(x-1\right)\left(x-2\right)^{2}.
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}