Solve (2/11x^{5}-8/19x^{4}+3/41x^3)-(5/3x^5+frac{3}{76}x^4-frac{5}{2}x^3)

$$( \frac { 2 } { 11 } x ^ { 5 } - \frac { 8 } { 19 } x ^ { 4 } + \frac { 3 } { 41 } x ^ { 3 } ) - ( \frac { 5 } { 3 } x ^ { 5 } + \frac { 3 } { 76 } x ^ { 4 } - \frac { 5 } { 2 } x ^ { 3 } )$$

Evaluate

$$-\frac{49x^{5}}{33}-\frac{35x^{4}}{76}+\frac{211x^{3}}{82}$$

Solution Steps

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.

$$\frac{2}{11}x^{5}-\frac{8}{19}x^{4}+\frac{3}{41}x^{3}-\frac{5}{3}x^{5}-\frac{3}{76}x^{4}+\frac{5}{2}x^{3}$$

Combine \frac{2}{11}x^{5} and -\frac{5}{3}x^{5} to get -\frac{49}{33}x^{5}.

$$-\frac{49}{33}x^{5}-\frac{8}{19}x^{4}+\frac{3}{41}x^{3}-\frac{3}{76}x^{4}+\frac{5}{2}x^{3}$$

Combine -\frac{8}{19}x^{4} and -\frac{3}{76}x^{4} to get -\frac{35}{76}x^{4}.

$$-\frac{49}{33}x^{5}-\frac{35}{76}x^{4}+\frac{3}{41}x^{3}+\frac{5}{2}x^{3}$$

Combine \frac{3}{41}x^{3} and \frac{5}{2}x^{3} to get \frac{211}{82}x^{3}.

$$-\frac{49}{33}x^{5}-\frac{35}{76}x^{4}+\frac{211}{82}x^{3}$$

Expand

$$-\frac{49x^{5}}{33}-\frac{35x^{4}}{76}+\frac{211x^{3}}{82}$$

Solution Steps

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.

$$\frac{2}{11}x^{5}-\frac{8}{19}x^{4}+\frac{3}{41}x^{3}-\frac{5}{3}x^{5}-\frac{3}{76}x^{4}+\frac{5}{2}x^{3}$$

Combine \frac{2}{11}x^{5} and -\frac{5}{3}x^{5} to get -\frac{49}{33}x^{5}.

$$-\frac{49}{33}x^{5}-\frac{8}{19}x^{4}+\frac{3}{41}x^{3}-\frac{3}{76}x^{4}+\frac{5}{2}x^{3}$$

Combine -\frac{8}{19}x^{4} and -\frac{3}{76}x^{4} to get -\frac{35}{76}x^{4}.

$$-\frac{49}{33}x^{5}-\frac{35}{76}x^{4}+\frac{3}{41}x^{3}+\frac{5}{2}x^{3}$$

Combine \frac{3}{41}x^{3} and \frac{5}{2}x^{3} to get \frac{211}{82}x^{3}.

$$-\frac{49}{33}x^{5}-\frac{35}{76}x^{4}+\frac{211}{82}x^{3}$$