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\frac{4m^{2}+9m-12}{4m\left(m+4\right)}
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\frac{4m^{2}+9m-12}{4m\left(m+4\right)}
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\frac{\left(m+3\right)\times 4m}{4m\left(m+4\right)}-\frac{3\left(m+4\right)}{4m\left(m+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4+m and 4m is 4m\left(m+4\right). Multiply \frac{m+3}{4+m} times \frac{4m}{4m}. Multiply \frac{3}{4m} times \frac{m+4}{m+4}.
\frac{\left(m+3\right)\times 4m-3\left(m+4\right)}{4m\left(m+4\right)}
Since \frac{\left(m+3\right)\times 4m}{4m\left(m+4\right)} and \frac{3\left(m+4\right)}{4m\left(m+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4m^{2}+12m-3m-12}{4m\left(m+4\right)}
Do the multiplications in \left(m+3\right)\times 4m-3\left(m+4\right).
\frac{4m^{2}+9m-12}{4m\left(m+4\right)}
Combine like terms in 4m^{2}+12m-3m-12.
\frac{4\left(m-\left(-\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{4m\left(m+4\right)}
Factor the expressions that are not already factored in \frac{4m^{2}+9m-12}{4m\left(m+4\right)}.
\frac{\left(m-\left(-\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{m\left(m+4\right)}
Cancel out 4 in both numerator and denominator.
\frac{\left(m-\left(-\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{m^{2}+4m}
Expand m\left(m+4\right).
\frac{\left(m-\left(-\frac{1}{8}\sqrt{273}\right)-\left(-\frac{9}{8}\right)\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{m^{2}+4m}
To find the opposite of -\frac{1}{8}\sqrt{273}-\frac{9}{8}, find the opposite of each term.
\frac{\left(m+\frac{1}{8}\sqrt{273}-\left(-\frac{9}{8}\right)\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{m^{2}+4m}
The opposite of -\frac{1}{8}\sqrt{273} is \frac{1}{8}\sqrt{273}.
\frac{\left(m+\frac{1}{8}\sqrt{273}+\frac{9}{8}\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{m^{2}+4m}
The opposite of -\frac{9}{8} is \frac{9}{8}.
\frac{\left(m+\frac{1}{8}\sqrt{273}+\frac{9}{8}\right)\left(m-\frac{1}{8}\sqrt{273}-\left(-\frac{9}{8}\right)\right)}{m^{2}+4m}
To find the opposite of \frac{1}{8}\sqrt{273}-\frac{9}{8}, find the opposite of each term.
\frac{\left(m+\frac{1}{8}\sqrt{273}+\frac{9}{8}\right)\left(m-\frac{1}{8}\sqrt{273}+\frac{9}{8}\right)}{m^{2}+4m}
The opposite of -\frac{9}{8} is \frac{9}{8}.
\frac{m^{2}+m\left(-\frac{1}{8}\right)\sqrt{273}+m\times \frac{9}{8}+\frac{1}{8}\sqrt{273}m+\frac{1}{8}\sqrt{273}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Apply the distributive property by multiplying each term of m+\frac{1}{8}\sqrt{273}+\frac{9}{8} by each term of m-\frac{1}{8}\sqrt{273}+\frac{9}{8}.
\frac{m^{2}+m\left(-\frac{1}{8}\right)\sqrt{273}+m\times \frac{9}{8}+\frac{1}{8}\sqrt{273}m+\frac{1}{8}\times 273\left(-\frac{1}{8}\right)+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Multiply \sqrt{273} and \sqrt{273} to get 273.
\frac{m^{2}+m\times \frac{9}{8}+\frac{1}{8}\times 273\left(-\frac{1}{8}\right)+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Combine m\left(-\frac{1}{8}\right)\sqrt{273} and \frac{1}{8}\sqrt{273}m to get 0.
\frac{m^{2}+m\times \frac{9}{8}+\frac{273}{8}\left(-\frac{1}{8}\right)+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Multiply \frac{1}{8} and 273 to get \frac{273}{8}.
\frac{m^{2}+m\times \frac{9}{8}+\frac{273\left(-1\right)}{8\times 8}+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Multiply \frac{273}{8} times -\frac{1}{8} by multiplying numerator times numerator and denominator times denominator.
\frac{m^{2}+m\times \frac{9}{8}+\frac{-273}{64}+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Do the multiplications in the fraction \frac{273\left(-1\right)}{8\times 8}.
\frac{m^{2}+m\times \frac{9}{8}-\frac{273}{64}+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Fraction \frac{-273}{64} can be rewritten as -\frac{273}{64} by extracting the negative sign.
\frac{m^{2}+m\times \frac{9}{8}-\frac{273}{64}+\frac{1\times 9}{8\times 8}\sqrt{273}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Multiply \frac{1}{8} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.
\frac{m^{2}+m\times \frac{9}{8}-\frac{273}{64}+\frac{9}{64}\sqrt{273}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Do the multiplications in the fraction \frac{1\times 9}{8\times 8}.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9}{64}\sqrt{273}+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Combine m\times \frac{9}{8} and \frac{9}{8}m to get \frac{9}{4}m.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9}{64}\sqrt{273}+\frac{9\left(-1\right)}{8\times 8}\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Multiply \frac{9}{8} times -\frac{1}{8} by multiplying numerator times numerator and denominator times denominator.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9}{64}\sqrt{273}+\frac{-9}{64}\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Do the multiplications in the fraction \frac{9\left(-1\right)}{8\times 8}.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9}{64}\sqrt{273}-\frac{9}{64}\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Fraction \frac{-9}{64} can be rewritten as -\frac{9}{64} by extracting the negative sign.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Combine \frac{9}{64}\sqrt{273} and -\frac{9}{64}\sqrt{273} to get 0.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9\times 9}{8\times 8}}{m^{2}+4m}
Multiply \frac{9}{8} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{81}{64}}{m^{2}+4m}
Do the multiplications in the fraction \frac{9\times 9}{8\times 8}.
\frac{m^{2}+\frac{9}{4}m+\frac{-273+81}{64}}{m^{2}+4m}
Since -\frac{273}{64} and \frac{81}{64} have the same denominator, add them by adding their numerators.
\frac{m^{2}+\frac{9}{4}m+\frac{-192}{64}}{m^{2}+4m}
Add -273 and 81 to get -192.
\frac{m^{2}+\frac{9}{4}m-3}{m^{2}+4m}
Divide -192 by 64 to get -3.
\frac{\left(m+3\right)\times 4m}{4m\left(m+4\right)}-\frac{3\left(m+4\right)}{4m\left(m+4\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4+m and 4m is 4m\left(m+4\right). Multiply \frac{m+3}{4+m} times \frac{4m}{4m}. Multiply \frac{3}{4m} times \frac{m+4}{m+4}.
\frac{\left(m+3\right)\times 4m-3\left(m+4\right)}{4m\left(m+4\right)}
Since \frac{\left(m+3\right)\times 4m}{4m\left(m+4\right)} and \frac{3\left(m+4\right)}{4m\left(m+4\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4m^{2}+12m-3m-12}{4m\left(m+4\right)}
Do the multiplications in \left(m+3\right)\times 4m-3\left(m+4\right).
\frac{4m^{2}+9m-12}{4m\left(m+4\right)}
Combine like terms in 4m^{2}+12m-3m-12.
\frac{4\left(m-\left(-\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{4m\left(m+4\right)}
Factor the expressions that are not already factored in \frac{4m^{2}+9m-12}{4m\left(m+4\right)}.
\frac{\left(m-\left(-\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{m\left(m+4\right)}
Cancel out 4 in both numerator and denominator.
\frac{\left(m-\left(-\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{m^{2}+4m}
Expand m\left(m+4\right).
\frac{\left(m-\left(-\frac{1}{8}\sqrt{273}\right)-\left(-\frac{9}{8}\right)\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{m^{2}+4m}
To find the opposite of -\frac{1}{8}\sqrt{273}-\frac{9}{8}, find the opposite of each term.
\frac{\left(m+\frac{1}{8}\sqrt{273}-\left(-\frac{9}{8}\right)\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{m^{2}+4m}
The opposite of -\frac{1}{8}\sqrt{273} is \frac{1}{8}\sqrt{273}.
\frac{\left(m+\frac{1}{8}\sqrt{273}+\frac{9}{8}\right)\left(m-\left(\frac{1}{8}\sqrt{273}-\frac{9}{8}\right)\right)}{m^{2}+4m}
The opposite of -\frac{9}{8} is \frac{9}{8}.
\frac{\left(m+\frac{1}{8}\sqrt{273}+\frac{9}{8}\right)\left(m-\frac{1}{8}\sqrt{273}-\left(-\frac{9}{8}\right)\right)}{m^{2}+4m}
To find the opposite of \frac{1}{8}\sqrt{273}-\frac{9}{8}, find the opposite of each term.
\frac{\left(m+\frac{1}{8}\sqrt{273}+\frac{9}{8}\right)\left(m-\frac{1}{8}\sqrt{273}+\frac{9}{8}\right)}{m^{2}+4m}
The opposite of -\frac{9}{8} is \frac{9}{8}.
\frac{m^{2}+m\left(-\frac{1}{8}\right)\sqrt{273}+m\times \frac{9}{8}+\frac{1}{8}\sqrt{273}m+\frac{1}{8}\sqrt{273}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Apply the distributive property by multiplying each term of m+\frac{1}{8}\sqrt{273}+\frac{9}{8} by each term of m-\frac{1}{8}\sqrt{273}+\frac{9}{8}.
\frac{m^{2}+m\left(-\frac{1}{8}\right)\sqrt{273}+m\times \frac{9}{8}+\frac{1}{8}\sqrt{273}m+\frac{1}{8}\times 273\left(-\frac{1}{8}\right)+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Multiply \sqrt{273} and \sqrt{273} to get 273.
\frac{m^{2}+m\times \frac{9}{8}+\frac{1}{8}\times 273\left(-\frac{1}{8}\right)+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Combine m\left(-\frac{1}{8}\right)\sqrt{273} and \frac{1}{8}\sqrt{273}m to get 0.
\frac{m^{2}+m\times \frac{9}{8}+\frac{273}{8}\left(-\frac{1}{8}\right)+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Multiply \frac{1}{8} and 273 to get \frac{273}{8}.
\frac{m^{2}+m\times \frac{9}{8}+\frac{273\left(-1\right)}{8\times 8}+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Multiply \frac{273}{8} times -\frac{1}{8} by multiplying numerator times numerator and denominator times denominator.
\frac{m^{2}+m\times \frac{9}{8}+\frac{-273}{64}+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Do the multiplications in the fraction \frac{273\left(-1\right)}{8\times 8}.
\frac{m^{2}+m\times \frac{9}{8}-\frac{273}{64}+\frac{1}{8}\sqrt{273}\times \frac{9}{8}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Fraction \frac{-273}{64} can be rewritten as -\frac{273}{64} by extracting the negative sign.
\frac{m^{2}+m\times \frac{9}{8}-\frac{273}{64}+\frac{1\times 9}{8\times 8}\sqrt{273}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Multiply \frac{1}{8} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.
\frac{m^{2}+m\times \frac{9}{8}-\frac{273}{64}+\frac{9}{64}\sqrt{273}+\frac{9}{8}m+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Do the multiplications in the fraction \frac{1\times 9}{8\times 8}.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9}{64}\sqrt{273}+\frac{9}{8}\left(-\frac{1}{8}\right)\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Combine m\times \frac{9}{8} and \frac{9}{8}m to get \frac{9}{4}m.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9}{64}\sqrt{273}+\frac{9\left(-1\right)}{8\times 8}\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Multiply \frac{9}{8} times -\frac{1}{8} by multiplying numerator times numerator and denominator times denominator.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9}{64}\sqrt{273}+\frac{-9}{64}\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Do the multiplications in the fraction \frac{9\left(-1\right)}{8\times 8}.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9}{64}\sqrt{273}-\frac{9}{64}\sqrt{273}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Fraction \frac{-9}{64} can be rewritten as -\frac{9}{64} by extracting the negative sign.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9}{8}\times \frac{9}{8}}{m^{2}+4m}
Combine \frac{9}{64}\sqrt{273} and -\frac{9}{64}\sqrt{273} to get 0.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{9\times 9}{8\times 8}}{m^{2}+4m}
Multiply \frac{9}{8} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.
\frac{m^{2}+\frac{9}{4}m-\frac{273}{64}+\frac{81}{64}}{m^{2}+4m}
Do the multiplications in the fraction \frac{9\times 9}{8\times 8}.
\frac{m^{2}+\frac{9}{4}m+\frac{-273+81}{64}}{m^{2}+4m}
Since -\frac{273}{64} and \frac{81}{64} have the same denominator, add them by adding their numerators.
\frac{m^{2}+\frac{9}{4}m+\frac{-192}{64}}{m^{2}+4m}
Add -273 and 81 to get -192.
\frac{m^{2}+\frac{9}{4}m-3}{m^{2}+4m}
Divide -192 by 64 to get -3.
Examples
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{ 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}