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