Solve (1/16r^6+1/2r^3-11/12)+(5/16r^6+frac{13}{2}r^3+frac{9}{12})

$$( \frac { 1 } { 16 } r ^ { 6 } + \frac { 1 } { 2 } r ^ { 3 } - \frac { 11 } { 12 } ) + ( \frac { 5 } { 16 } r ^ { 6 } + \frac { 13 } { 2 } r ^ { 3 } + \frac { 9 } { 12 } )$$

Evaluate

$$\frac{3r^{6}}{8}+7r^{3}-\frac{1}{6}$$

Solution Steps

Combine \frac{1}{16}r^{6} and \frac{5}{16}r^{6} to get \frac{3}{8}r^{6}.

$$\frac{3}{8}r^{6}+\frac{1}{2}r^{3}-\frac{11}{12}+\frac{13}{2}r^{3}+\frac{9}{12}$$

Combine \frac{1}{2}r^{3} and \frac{13}{2}r^{3} to get 7r^{3}.

$$\frac{3}{8}r^{6}+7r^{3}-\frac{11}{12}+\frac{9}{12}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{3}{8}r^{6}+7r^{3}-\frac{11}{12}+\frac{3}{4}$$

Add -\frac{11}{12} and \frac{3}{4} to get -\frac{1}{6}.

$$\frac{3}{8}r^{6}+7r^{3}-\frac{1}{6}$$

Factor

$$\frac{3\left(r^{3}-\frac{-2\sqrt{197}-28}{3}\right)\left(r^{3}-\frac{2\sqrt{197}-28}{3}\right)}{8}$$