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\frac{x^{2}}{30}+1
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\frac{x^{2}}{30}+1
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\frac{1}{3}x^{2}-\frac{1}{2}x^{2}+2x+\frac{1}{2}-\left(\frac{5}{6}x-\frac{1}{5}x^{2}-1\right)-\left(\frac{7}{6}x+\frac{1}{2}\right)
Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.
-\frac{1}{6}x^{2}+2x+\frac{1}{2}-\left(\frac{5}{6}x-\frac{1}{5}x^{2}-1\right)-\left(\frac{7}{6}x+\frac{1}{2}\right)
Combine \frac{1}{3}x^{2} and -\frac{1}{2}x^{2} to get -\frac{1}{6}x^{2}.
-\frac{1}{6}x^{2}+2x+\frac{1}{2}-\frac{5}{6}x+\frac{1}{5}x^{2}+1-\left(\frac{7}{6}x+\frac{1}{2}\right)
To find the opposite of \frac{5}{6}x-\frac{1}{5}x^{2}-1, find the opposite of each term.
-\frac{1}{6}x^{2}+\frac{7}{6}x+\frac{1}{2}+\frac{1}{5}x^{2}+1-\left(\frac{7}{6}x+\frac{1}{2}\right)
Combine 2x and -\frac{5}{6}x to get \frac{7}{6}x.
\frac{1}{30}x^{2}+\frac{7}{6}x+\frac{1}{2}+1-\left(\frac{7}{6}x+\frac{1}{2}\right)
Combine -\frac{1}{6}x^{2} and \frac{1}{5}x^{2} to get \frac{1}{30}x^{2}.
\frac{1}{30}x^{2}+\frac{7}{6}x+\frac{3}{2}-\left(\frac{7}{6}x+\frac{1}{2}\right)
Add \frac{1}{2} and 1 to get \frac{3}{2}.
\frac{1}{30}x^{2}+\frac{7}{6}x+\frac{3}{2}-\frac{7}{6}x-\frac{1}{2}
To find the opposite of \frac{7}{6}x+\frac{1}{2}, find the opposite of each term.
\frac{1}{30}x^{2}+\frac{3}{2}-\frac{1}{2}
Combine \frac{7}{6}x and -\frac{7}{6}x to get 0.
\frac{1}{30}x^{2}+1
Subtract \frac{1}{2} from \frac{3}{2} to get 1.
\frac{1}{3}x^{2}-\frac{1}{2}x^{2}+2x+\frac{1}{2}-\left(\frac{5}{6}x-\frac{1}{5}x^{2}-1\right)-\left(\frac{7}{6}x+\frac{1}{2}\right)
Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.
-\frac{1}{6}x^{2}+2x+\frac{1}{2}-\left(\frac{5}{6}x-\frac{1}{5}x^{2}-1\right)-\left(\frac{7}{6}x+\frac{1}{2}\right)
Combine \frac{1}{3}x^{2} and -\frac{1}{2}x^{2} to get -\frac{1}{6}x^{2}.
-\frac{1}{6}x^{2}+2x+\frac{1}{2}-\frac{5}{6}x+\frac{1}{5}x^{2}+1-\left(\frac{7}{6}x+\frac{1}{2}\right)
To find the opposite of \frac{5}{6}x-\frac{1}{5}x^{2}-1, find the opposite of each term.
-\frac{1}{6}x^{2}+\frac{7}{6}x+\frac{1}{2}+\frac{1}{5}x^{2}+1-\left(\frac{7}{6}x+\frac{1}{2}\right)
Combine 2x and -\frac{5}{6}x to get \frac{7}{6}x.
\frac{1}{30}x^{2}+\frac{7}{6}x+\frac{1}{2}+1-\left(\frac{7}{6}x+\frac{1}{2}\right)
Combine -\frac{1}{6}x^{2} and \frac{1}{5}x^{2} to get \frac{1}{30}x^{2}.
\frac{1}{30}x^{2}+\frac{7}{6}x+\frac{3}{2}-\left(\frac{7}{6}x+\frac{1}{2}\right)
Add \frac{1}{2} and 1 to get \frac{3}{2}.
\frac{1}{30}x^{2}+\frac{7}{6}x+\frac{3}{2}-\frac{7}{6}x-\frac{1}{2}
To find the opposite of \frac{7}{6}x+\frac{1}{2}, find the opposite of each term.
\frac{1}{30}x^{2}+\frac{3}{2}-\frac{1}{2}
Combine \frac{7}{6}x and -\frac{7}{6}x to get 0.
\frac{1}{30}x^{2}+1
Subtract \frac{1}{2} from \frac{3}{2} to get 1.
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
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Limits
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