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Arithmetic
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\frac { 3 } { 5 } - \frac { 7 } { 1 } = 3 \times 7 - 5 \times 7 =
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\frac{3}{5}-7=3\times 7-5\times 7
Anything divided by one gives itself.
\frac{3}{5}-\frac{35}{5}=3\times 7-5\times 7
Convert 7 to fraction \frac{35}{5}.
\frac{3-35}{5}=3\times 7-5\times 7
Since \frac{3}{5} and \frac{35}{5} have the same denominator, subtract them by subtracting their numerators.
-\frac{32}{5}=3\times 7-5\times 7
Subtract 35 from 3 to get -32.
-\frac{32}{5}=21-5\times 7
Multiply 3 and 7 to get 21.
-\frac{32}{5}=21-35
Multiply 5 and 7 to get 35.
-\frac{32}{5}=-14
Subtract 35 from 21 to get -14.
-\frac{32}{5}=-\frac{70}{5}
Convert -14 to fraction -\frac{70}{5}.
\text{false}
Compare -\frac{32}{5} and -\frac{70}{5}.
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}