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\frac{1}{-m-3}
Expand
\frac{1}{-m-3}
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\frac{\frac{\left(m-3\right)\left(m-2\right)}{\left(m-2\right)^{2}}}{\frac{5}{m-2}-m-2}
Factor the expressions that are not already factored in \frac{m^{2}-5m+6}{m^{2}-4m+4}.
\frac{\frac{m-3}{m-2}}{\frac{5}{m-2}-m-2}
Cancel out m-2 in both numerator and denominator.
\frac{\frac{m-3}{m-2}}{\frac{5}{m-2}+\frac{\left(-m-2\right)\left(m-2\right)}{m-2}}
To add or subtract expressions, expand them to make their denominators the same. Multiply -m-2 times \frac{m-2}{m-2}.
\frac{\frac{m-3}{m-2}}{\frac{5+\left(-m-2\right)\left(m-2\right)}{m-2}}
Since \frac{5}{m-2} and \frac{\left(-m-2\right)\left(m-2\right)}{m-2} have the same denominator, add them by adding their numerators.
\frac{\frac{m-3}{m-2}}{\frac{5-m^{2}+2m-2m+4}{m-2}}
Do the multiplications in 5+\left(-m-2\right)\left(m-2\right).
\frac{\frac{m-3}{m-2}}{\frac{9-m^{2}}{m-2}}
Combine like terms in 5-m^{2}+2m-2m+4.
\frac{\left(m-3\right)\left(m-2\right)}{\left(m-2\right)\left(9-m^{2}\right)}
Divide \frac{m-3}{m-2} by \frac{9-m^{2}}{m-2} by multiplying \frac{m-3}{m-2} by the reciprocal of \frac{9-m^{2}}{m-2}.
\frac{m-3}{-m^{2}+9}
Cancel out m-2 in both numerator and denominator.
\frac{m-3}{\left(m-3\right)\left(-m-3\right)}
Factor the expressions that are not already factored.
\frac{1}{-m-3}
Cancel out m-3 in both numerator and denominator.
\frac{\frac{\left(m-3\right)\left(m-2\right)}{\left(m-2\right)^{2}}}{\frac{5}{m-2}-m-2}
Factor the expressions that are not already factored in \frac{m^{2}-5m+6}{m^{2}-4m+4}.
\frac{\frac{m-3}{m-2}}{\frac{5}{m-2}-m-2}
Cancel out m-2 in both numerator and denominator.
\frac{\frac{m-3}{m-2}}{\frac{5}{m-2}+\frac{\left(-m-2\right)\left(m-2\right)}{m-2}}
To add or subtract expressions, expand them to make their denominators the same. Multiply -m-2 times \frac{m-2}{m-2}.
\frac{\frac{m-3}{m-2}}{\frac{5+\left(-m-2\right)\left(m-2\right)}{m-2}}
Since \frac{5}{m-2} and \frac{\left(-m-2\right)\left(m-2\right)}{m-2} have the same denominator, add them by adding their numerators.
\frac{\frac{m-3}{m-2}}{\frac{5-m^{2}+2m-2m+4}{m-2}}
Do the multiplications in 5+\left(-m-2\right)\left(m-2\right).
\frac{\frac{m-3}{m-2}}{\frac{9-m^{2}}{m-2}}
Combine like terms in 5-m^{2}+2m-2m+4.
\frac{\left(m-3\right)\left(m-2\right)}{\left(m-2\right)\left(9-m^{2}\right)}
Divide \frac{m-3}{m-2} by \frac{9-m^{2}}{m-2} by multiplying \frac{m-3}{m-2} by the reciprocal of \frac{9-m^{2}}{m-2}.
\frac{m-3}{-m^{2}+9}
Cancel out m-2 in both numerator and denominator.
\frac{m-3}{\left(m-3\right)\left(-m-3\right)}
Factor the expressions that are not already factored.
\frac{1}{-m-3}
Cancel out m-3 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}