Evaluate
\frac{47d+18}{4\left(3d+2\right)}
Factor
\frac{47d+18}{4\left(3d+2\right)}
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\frac{9\left(3d+2\right)}{4\left(3d+2\right)}+\frac{4\times 5d}{4\left(3d+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3d+2 is 4\left(3d+2\right). Multiply \frac{9}{4} times \frac{3d+2}{3d+2}. Multiply \frac{5d}{3d+2} times \frac{4}{4}.
\frac{9\left(3d+2\right)+4\times 5d}{4\left(3d+2\right)}
Since \frac{9\left(3d+2\right)}{4\left(3d+2\right)} and \frac{4\times 5d}{4\left(3d+2\right)} have the same denominator, add them by adding their numerators.
\frac{27d+18+20d}{4\left(3d+2\right)}
Do the multiplications in 9\left(3d+2\right)+4\times 5d.
\frac{47d+18}{4\left(3d+2\right)}
Combine like terms in 27d+18+20d.
\frac{47d+18}{12d+8}
Expand 4\left(3d+2\right).
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y = 3x + 4
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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}