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\frac{1640}{41}+\frac{180}{41}=40+4\times 38\text{ and }40+4\times 38=44\times 38
Convert 40 to fraction \frac{1640}{41}.
\frac{1640+180}{41}=40+4\times 38\text{ and }40+4\times 38=44\times 38
Since \frac{1640}{41} and \frac{180}{41} have the same denominator, add them by adding their numerators.
\frac{1820}{41}=40+4\times 38\text{ and }40+4\times 38=44\times 38
Add 1640 and 180 to get 1820.
\frac{1820}{41}=40+152\text{ and }40+4\times 38=44\times 38
Multiply 4 and 38 to get 152.
\frac{1820}{41}=192\text{ and }40+4\times 38=44\times 38
Add 40 and 152 to get 192.
\frac{1820}{41}=\frac{7872}{41}\text{ and }40+4\times 38=44\times 38
Convert 192 to fraction \frac{7872}{41}.
\text{false}\text{ and }40+4\times 38=44\times 38
Compare \frac{1820}{41} and \frac{7872}{41}.
\text{false}\text{ and }40+152=44\times 38
Multiply 4 and 38 to get 152.
\text{false}\text{ and }192=44\times 38
Add 40 and 152 to get 192.
\text{false}\text{ and }192=1672
Multiply 44 and 38 to get 1672.
\text{false}\text{ and }\text{false}
Compare 192 and 1672.
\text{false}
The conjunction of \text{false} and \text{false} is \text{false}.
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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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}