Evaluate
\frac{-x^{2}+12x-16}{2\left(x-4\right)\left(x-1\right)}
Expand
-\frac{x^{2}-12x+16}{2\left(x-4\right)\left(x-1\right)}
Graph
Share
Copied to clipboard
\frac{\frac{x^{2}}{x-4}+\frac{2\left(x-4\right)}{x-4}}{2x-2}-1
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x-4}{x-4}.
\frac{\frac{x^{2}+2\left(x-4\right)}{x-4}}{2x-2}-1
Since \frac{x^{2}}{x-4} and \frac{2\left(x-4\right)}{x-4} have the same denominator, add them by adding their numerators.
\frac{\frac{x^{2}+2x-8}{x-4}}{2x-2}-1
Do the multiplications in x^{2}+2\left(x-4\right).
\frac{x^{2}+2x-8}{\left(x-4\right)\left(2x-2\right)}-1
Express \frac{\frac{x^{2}+2x-8}{x-4}}{2x-2} as a single fraction.
\frac{x^{2}+2x-8}{2\left(x-4\right)\left(x-1\right)}-1
Factor \left(x-4\right)\left(2x-2\right).
\frac{x^{2}+2x-8}{2\left(x-4\right)\left(x-1\right)}-\frac{2\left(x-4\right)\left(x-1\right)}{2\left(x-4\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2\left(x-4\right)\left(x-1\right)}{2\left(x-4\right)\left(x-1\right)}.
\frac{x^{2}+2x-8-2\left(x-4\right)\left(x-1\right)}{2\left(x-4\right)\left(x-1\right)}
Since \frac{x^{2}+2x-8}{2\left(x-4\right)\left(x-1\right)} and \frac{2\left(x-4\right)\left(x-1\right)}{2\left(x-4\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+2x-8-2x^{2}+2x+8x-8}{2\left(x-4\right)\left(x-1\right)}
Do the multiplications in x^{2}+2x-8-2\left(x-4\right)\left(x-1\right).
\frac{-x^{2}+12x-16}{2\left(x-4\right)\left(x-1\right)}
Combine like terms in x^{2}+2x-8-2x^{2}+2x+8x-8.
\frac{-x^{2}+12x-16}{2x^{2}-10x+8}
Expand 2\left(x-4\right)\left(x-1\right).
\frac{\frac{x^{2}}{x-4}+\frac{2\left(x-4\right)}{x-4}}{2x-2}-1
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x-4}{x-4}.
\frac{\frac{x^{2}+2\left(x-4\right)}{x-4}}{2x-2}-1
Since \frac{x^{2}}{x-4} and \frac{2\left(x-4\right)}{x-4} have the same denominator, add them by adding their numerators.
\frac{\frac{x^{2}+2x-8}{x-4}}{2x-2}-1
Do the multiplications in x^{2}+2\left(x-4\right).
\frac{x^{2}+2x-8}{\left(x-4\right)\left(2x-2\right)}-1
Express \frac{\frac{x^{2}+2x-8}{x-4}}{2x-2} as a single fraction.
\frac{x^{2}+2x-8}{2\left(x-4\right)\left(x-1\right)}-1
Factor \left(x-4\right)\left(2x-2\right).
\frac{x^{2}+2x-8}{2\left(x-4\right)\left(x-1\right)}-\frac{2\left(x-4\right)\left(x-1\right)}{2\left(x-4\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2\left(x-4\right)\left(x-1\right)}{2\left(x-4\right)\left(x-1\right)}.
\frac{x^{2}+2x-8-2\left(x-4\right)\left(x-1\right)}{2\left(x-4\right)\left(x-1\right)}
Since \frac{x^{2}+2x-8}{2\left(x-4\right)\left(x-1\right)} and \frac{2\left(x-4\right)\left(x-1\right)}{2\left(x-4\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+2x-8-2x^{2}+2x+8x-8}{2\left(x-4\right)\left(x-1\right)}
Do the multiplications in x^{2}+2x-8-2\left(x-4\right)\left(x-1\right).
\frac{-x^{2}+12x-16}{2\left(x-4\right)\left(x-1\right)}
Combine like terms in x^{2}+2x-8-2x^{2}+2x+8x-8.
\frac{-x^{2}+12x-16}{2x^{2}-10x+8}
Expand 2\left(x-4\right)\left(x-1\right).
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}