Evaluate
-\frac{2}{7}+\frac{17}{21d}
Expand
-\frac{2}{7}+\frac{17}{21d}
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\frac{3\left(5d+1\right)}{21d}-\frac{7\left(3d-2\right)}{21d}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7d and 3d is 21d. Multiply \frac{5d+1}{7d} times \frac{3}{3}. Multiply \frac{3d-2}{3d} times \frac{7}{7}.
\frac{3\left(5d+1\right)-7\left(3d-2\right)}{21d}
Since \frac{3\left(5d+1\right)}{21d} and \frac{7\left(3d-2\right)}{21d} have the same denominator, subtract them by subtracting their numerators.
\frac{15d+3-21d+14}{21d}
Do the multiplications in 3\left(5d+1\right)-7\left(3d-2\right).
\frac{-6d+17}{21d}
Combine like terms in 15d+3-21d+14.
\frac{3\left(5d+1\right)}{21d}-\frac{7\left(3d-2\right)}{21d}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7d and 3d is 21d. Multiply \frac{5d+1}{7d} times \frac{3}{3}. Multiply \frac{3d-2}{3d} times \frac{7}{7}.
\frac{3\left(5d+1\right)-7\left(3d-2\right)}{21d}
Since \frac{3\left(5d+1\right)}{21d} and \frac{7\left(3d-2\right)}{21d} have the same denominator, subtract them by subtracting their numerators.
\frac{15d+3-21d+14}{21d}
Do the multiplications in 3\left(5d+1\right)-7\left(3d-2\right).
\frac{-6d+17}{21d}
Combine like terms in 15d+3-21d+14.
Examples
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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}