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-\frac{x}{12}
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-\frac{x}{12}
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\frac{1}{4}\times 3x+\frac{1}{4}\left(-2\right)-\frac{1}{6}\left(5x-3\right)
Use the distributive property to multiply \frac{1}{4} by 3x-2.
\frac{3}{4}x+\frac{1}{4}\left(-2\right)-\frac{1}{6}\left(5x-3\right)
Multiply \frac{1}{4} and 3 to get \frac{3}{4}.
\frac{3}{4}x+\frac{-2}{4}-\frac{1}{6}\left(5x-3\right)
Multiply \frac{1}{4} and -2 to get \frac{-2}{4}.
\frac{3}{4}x-\frac{1}{2}-\frac{1}{6}\left(5x-3\right)
Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.
\frac{3}{4}x-\frac{1}{2}-\frac{1}{6}\times 5x-\frac{1}{6}\left(-3\right)
Use the distributive property to multiply -\frac{1}{6} by 5x-3.
\frac{3}{4}x-\frac{1}{2}+\frac{-5}{6}x-\frac{1}{6}\left(-3\right)
Express -\frac{1}{6}\times 5 as a single fraction.
\frac{3}{4}x-\frac{1}{2}-\frac{5}{6}x-\frac{1}{6}\left(-3\right)
Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.
\frac{3}{4}x-\frac{1}{2}-\frac{5}{6}x+\frac{-\left(-3\right)}{6}
Express -\frac{1}{6}\left(-3\right) as a single fraction.
\frac{3}{4}x-\frac{1}{2}-\frac{5}{6}x+\frac{3}{6}
Multiply -1 and -3 to get 3.
\frac{3}{4}x-\frac{1}{2}-\frac{5}{6}x+\frac{1}{2}
Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.
-\frac{1}{12}x-\frac{1}{2}+\frac{1}{2}
Combine \frac{3}{4}x and -\frac{5}{6}x to get -\frac{1}{12}x.
-\frac{1}{12}x
Add -\frac{1}{2} and \frac{1}{2} to get 0.
\frac{1}{4}\times 3x+\frac{1}{4}\left(-2\right)-\frac{1}{6}\left(5x-3\right)
Use the distributive property to multiply \frac{1}{4} by 3x-2.
\frac{3}{4}x+\frac{1}{4}\left(-2\right)-\frac{1}{6}\left(5x-3\right)
Multiply \frac{1}{4} and 3 to get \frac{3}{4}.
\frac{3}{4}x+\frac{-2}{4}-\frac{1}{6}\left(5x-3\right)
Multiply \frac{1}{4} and -2 to get \frac{-2}{4}.
\frac{3}{4}x-\frac{1}{2}-\frac{1}{6}\left(5x-3\right)
Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.
\frac{3}{4}x-\frac{1}{2}-\frac{1}{6}\times 5x-\frac{1}{6}\left(-3\right)
Use the distributive property to multiply -\frac{1}{6} by 5x-3.
\frac{3}{4}x-\frac{1}{2}+\frac{-5}{6}x-\frac{1}{6}\left(-3\right)
Express -\frac{1}{6}\times 5 as a single fraction.
\frac{3}{4}x-\frac{1}{2}-\frac{5}{6}x-\frac{1}{6}\left(-3\right)
Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.
\frac{3}{4}x-\frac{1}{2}-\frac{5}{6}x+\frac{-\left(-3\right)}{6}
Express -\frac{1}{6}\left(-3\right) as a single fraction.
\frac{3}{4}x-\frac{1}{2}-\frac{5}{6}x+\frac{3}{6}
Multiply -1 and -3 to get 3.
\frac{3}{4}x-\frac{1}{2}-\frac{5}{6}x+\frac{1}{2}
Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.
-\frac{1}{12}x-\frac{1}{2}+\frac{1}{2}
Combine \frac{3}{4}x and -\frac{5}{6}x to get -\frac{1}{12}x.
-\frac{1}{12}x
Add -\frac{1}{2} and \frac{1}{2} to get 0.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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