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