Evaluate
-\frac{2x^{5}}{3}-\frac{67x^{4}}{76}+\frac{217x^{3}}{82}
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-\frac{2x^{5}}{3}-\frac{67x^{4}}{76}+\frac{217x^{3}}{82}
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2\left(\frac{1}{2}x^{5}-\frac{8}{19}x^{4}+\frac{3}{41}x^{3}\right)-\left(\frac{5}{3}x^{5}+\frac{3}{76}x^{4}-\frac{5}{2}x^{3}\right)
Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.
x^{5}-\frac{16}{19}x^{4}+\frac{6}{41}x^{3}-\left(\frac{5}{3}x^{5}+\frac{3}{76}x^{4}-\frac{5}{2}x^{3}\right)
Use the distributive property to multiply 2 by \frac{1}{2}x^{5}-\frac{8}{19}x^{4}+\frac{3}{41}x^{3}.
x^{5}-\frac{16}{19}x^{4}+\frac{6}{41}x^{3}-\frac{5}{3}x^{5}-\frac{3}{76}x^{4}+\frac{5}{2}x^{3}
To find the opposite of \frac{5}{3}x^{5}+\frac{3}{76}x^{4}-\frac{5}{2}x^{3}, find the opposite of each term.
-\frac{2}{3}x^{5}-\frac{16}{19}x^{4}+\frac{6}{41}x^{3}-\frac{3}{76}x^{4}+\frac{5}{2}x^{3}
Combine x^{5} and -\frac{5}{3}x^{5} to get -\frac{2}{3}x^{5}.
-\frac{2}{3}x^{5}-\frac{67}{76}x^{4}+\frac{6}{41}x^{3}+\frac{5}{2}x^{3}
Combine -\frac{16}{19}x^{4} and -\frac{3}{76}x^{4} to get -\frac{67}{76}x^{4}.
-\frac{2}{3}x^{5}-\frac{67}{76}x^{4}+\frac{217}{82}x^{3}
Combine \frac{6}{41}x^{3} and \frac{5}{2}x^{3} to get \frac{217}{82}x^{3}.
2\left(\frac{1}{2}x^{5}-\frac{8}{19}x^{4}+\frac{3}{41}x^{3}\right)-\left(\frac{5}{3}x^{5}+\frac{3}{76}x^{4}-\frac{5}{2}x^{3}\right)
Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.
x^{5}-\frac{16}{19}x^{4}+\frac{6}{41}x^{3}-\left(\frac{5}{3}x^{5}+\frac{3}{76}x^{4}-\frac{5}{2}x^{3}\right)
Use the distributive property to multiply 2 by \frac{1}{2}x^{5}-\frac{8}{19}x^{4}+\frac{3}{41}x^{3}.
x^{5}-\frac{16}{19}x^{4}+\frac{6}{41}x^{3}-\frac{5}{3}x^{5}-\frac{3}{76}x^{4}+\frac{5}{2}x^{3}
To find the opposite of \frac{5}{3}x^{5}+\frac{3}{76}x^{4}-\frac{5}{2}x^{3}, find the opposite of each term.
-\frac{2}{3}x^{5}-\frac{16}{19}x^{4}+\frac{6}{41}x^{3}-\frac{3}{76}x^{4}+\frac{5}{2}x^{3}
Combine x^{5} and -\frac{5}{3}x^{5} to get -\frac{2}{3}x^{5}.
-\frac{2}{3}x^{5}-\frac{67}{76}x^{4}+\frac{6}{41}x^{3}+\frac{5}{2}x^{3}
Combine -\frac{16}{19}x^{4} and -\frac{3}{76}x^{4} to get -\frac{67}{76}x^{4}.
-\frac{2}{3}x^{5}-\frac{67}{76}x^{4}+\frac{217}{82}x^{3}
Combine \frac{6}{41}x^{3} and \frac{5}{2}x^{3} to get \frac{217}{82}x^{3}.
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