Solve 7/2a^4-1/4a/frac{2{7a^2}+7/21a}

$$\frac { \frac { 7 } { 2 a ^ { 4 } } - \frac { 1 } { 4 a } } { \frac { 2 } { 7 a ^ { 2 } } + \frac { 7 } { 21 a } }$$

Evaluate

$$-\frac{21\left(a^{3}-14\right)}{4\left(7a+6\right)a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a^{4} and 4a is 4a^{4}. Multiply \frac{7}{2a^{4}} times \frac{2}{2}. Multiply \frac{1}{4a} times \frac{a^{3}}{a^{3}}.

$$\frac{\frac{7\times 2}{4a^{4}}-\frac{a^{3}}{4a^{4}}}{\frac{2}{7a^{2}}+\frac{7}{21a}}$$

Since \frac{7\times 2}{4a^{4}} and \frac{a^{3}}{4a^{4}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7\times 2-a^{3}}{4a^{4}}}{\frac{2}{7a^{2}}+\frac{7}{21a}}$$

Do the multiplications in 7\times 2-a^{3}.

$$\frac{\frac{14-a^{3}}{4a^{4}}}{\frac{2}{7a^{2}}+\frac{7}{21a}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7a^{2} and 21a is 21a^{2}. Multiply \frac{2}{7a^{2}} times \frac{3}{3}. Multiply \frac{7}{21a} times \frac{a}{a}.

$$\frac{\frac{14-a^{3}}{4a^{4}}}{\frac{2\times 3}{21a^{2}}+\frac{7a}{21a^{2}}}$$

Since \frac{2\times 3}{21a^{2}} and \frac{7a}{21a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{14-a^{3}}{4a^{4}}}{\frac{2\times 3+7a}{21a^{2}}}$$

Do the multiplications in 2\times 3+7a.

$$\frac{\frac{14-a^{3}}{4a^{4}}}{\frac{6+7a}{21a^{2}}}$$

Divide \frac{14-a^{3}}{4a^{4}} by \frac{6+7a}{21a^{2}} by multiplying \frac{14-a^{3}}{4a^{4}} by the reciprocal of \frac{6+7a}{21a^{2}}.

$$\frac{\left(14-a^{3}\right)\times 21a^{2}}{4a^{4}\left(6+7a\right)}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{21\left(-a^{3}+14\right)}{4\left(7a+6\right)a^{2}}$$

Use the distributive property to multiply 21 by -a^{3}+14.

$$\frac{-21a^{3}+294}{4\left(7a+6\right)a^{2}}$$

Use the distributive property to multiply 4 by 7a+6.

$$\frac{-21a^{3}+294}{\left(28a+24\right)a^{2}}$$

Use the distributive property to multiply 28a+24 by a^{2}.

$$\frac{-21a^{3}+294}{28a^{3}+24a^{2}}$$

Expand

$$-\frac{21\left(a^{3}-14\right)}{4\left(7a+6\right)a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2a^{4} and 4a is 4a^{4}. Multiply \frac{7}{2a^{4}} times \frac{2}{2}. Multiply \frac{1}{4a} times \frac{a^{3}}{a^{3}}.

$$\frac{\frac{7\times 2}{4a^{4}}-\frac{a^{3}}{4a^{4}}}{\frac{2}{7a^{2}}+\frac{7}{21a}}$$

Since \frac{7\times 2}{4a^{4}} and \frac{a^{3}}{4a^{4}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7\times 2-a^{3}}{4a^{4}}}{\frac{2}{7a^{2}}+\frac{7}{21a}}$$

Do the multiplications in 7\times 2-a^{3}.

$$\frac{\frac{14-a^{3}}{4a^{4}}}{\frac{2}{7a^{2}}+\frac{7}{21a}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7a^{2} and 21a is 21a^{2}. Multiply \frac{2}{7a^{2}} times \frac{3}{3}. Multiply \frac{7}{21a} times \frac{a}{a}.

$$\frac{\frac{14-a^{3}}{4a^{4}}}{\frac{2\times 3}{21a^{2}}+\frac{7a}{21a^{2}}}$$

Since \frac{2\times 3}{21a^{2}} and \frac{7a}{21a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{14-a^{3}}{4a^{4}}}{\frac{2\times 3+7a}{21a^{2}}}$$

Do the multiplications in 2\times 3+7a.

$$\frac{\frac{14-a^{3}}{4a^{4}}}{\frac{6+7a}{21a^{2}}}$$

Divide \frac{14-a^{3}}{4a^{4}} by \frac{6+7a}{21a^{2}} by multiplying \frac{14-a^{3}}{4a^{4}} by the reciprocal of \frac{6+7a}{21a^{2}}.

$$\frac{\left(14-a^{3}\right)\times 21a^{2}}{4a^{4}\left(6+7a\right)}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{21\left(-a^{3}+14\right)}{4\left(7a+6\right)a^{2}}$$

Use the distributive property to multiply 21 by -a^{3}+14.

$$\frac{-21a^{3}+294}{4\left(7a+6\right)a^{2}}$$

Use the distributive property to multiply 4 by 7a+6.

$$\frac{-21a^{3}+294}{\left(28a+24\right)a^{2}}$$

Use the distributive property to multiply 28a+24 by a^{2}.

$$\frac{-21a^{3}+294}{28a^{3}+24a^{2}}$$