Evaluate
-\frac{4}{\left(x-3\right)\left(x-1\right)}
Expand
-\frac{4}{\left(x-3\right)\left(x-1\right)}
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\frac{1}{x-1}-\frac{\left(x-3\right)\left(x^{2}+2x+1\right)}{\left(x^{2}-1\right)\left(x^{2}-6x+9\right)}
Multiply \frac{x-3}{x^{2}-1} times \frac{x^{2}+2x+1}{x^{2}-6x+9} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{x-1}-\frac{\left(x-3\right)\left(x+1\right)^{2}}{\left(x-1\right)\left(x+1\right)\left(x-3\right)^{2}}
Factor the expressions that are not already factored in \frac{\left(x-3\right)\left(x^{2}+2x+1\right)}{\left(x^{2}-1\right)\left(x^{2}-6x+9\right)}.
\frac{1}{x-1}-\frac{x+1}{\left(x-3\right)\left(x-1\right)}
Cancel out \left(x-3\right)\left(x+1\right) in both numerator and denominator.
\frac{x-3}{\left(x-3\right)\left(x-1\right)}-\frac{x+1}{\left(x-3\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x-3\right)\left(x-1\right) is \left(x-3\right)\left(x-1\right). Multiply \frac{1}{x-1} times \frac{x-3}{x-3}.
\frac{x-3-\left(x+1\right)}{\left(x-3\right)\left(x-1\right)}
Since \frac{x-3}{\left(x-3\right)\left(x-1\right)} and \frac{x+1}{\left(x-3\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x-3-x-1}{\left(x-3\right)\left(x-1\right)}
Do the multiplications in x-3-\left(x+1\right).
\frac{-4}{\left(x-3\right)\left(x-1\right)}
Combine like terms in x-3-x-1.
\frac{-4}{x^{2}-4x+3}
Expand \left(x-3\right)\left(x-1\right).
\frac{1}{x-1}-\frac{\left(x-3\right)\left(x^{2}+2x+1\right)}{\left(x^{2}-1\right)\left(x^{2}-6x+9\right)}
Multiply \frac{x-3}{x^{2}-1} times \frac{x^{2}+2x+1}{x^{2}-6x+9} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{x-1}-\frac{\left(x-3\right)\left(x+1\right)^{2}}{\left(x-1\right)\left(x+1\right)\left(x-3\right)^{2}}
Factor the expressions that are not already factored in \frac{\left(x-3\right)\left(x^{2}+2x+1\right)}{\left(x^{2}-1\right)\left(x^{2}-6x+9\right)}.
\frac{1}{x-1}-\frac{x+1}{\left(x-3\right)\left(x-1\right)}
Cancel out \left(x-3\right)\left(x+1\right) in both numerator and denominator.
\frac{x-3}{\left(x-3\right)\left(x-1\right)}-\frac{x+1}{\left(x-3\right)\left(x-1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x-3\right)\left(x-1\right) is \left(x-3\right)\left(x-1\right). Multiply \frac{1}{x-1} times \frac{x-3}{x-3}.
\frac{x-3-\left(x+1\right)}{\left(x-3\right)\left(x-1\right)}
Since \frac{x-3}{\left(x-3\right)\left(x-1\right)} and \frac{x+1}{\left(x-3\right)\left(x-1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x-3-x-1}{\left(x-3\right)\left(x-1\right)}
Do the multiplications in x-3-\left(x+1\right).
\frac{-4}{\left(x-3\right)\left(x-1\right)}
Combine like terms in x-3-x-1.
\frac{-4}{x^{2}-4x+3}
Expand \left(x-3\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}