Solve 7/5a^4-1/10a/frac{3{11a^2}+7/33a}

$$\frac { \frac { 7 } { 5 a ^ { 4 } } - \frac { 1 } { 10 a } } { \frac { 3 } { 11 a ^ { 2 } } + \frac { 7 } { 33 a } }$$

Evaluate

$$-\frac{33\left(a^{3}-14\right)}{10\left(7a+9\right)a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5a^{4} and 10a is 10a^{4}. Multiply \frac{7}{5a^{4}} times \frac{2}{2}. Multiply \frac{1}{10a} times \frac{a^{3}}{a^{3}}.

$$\frac{\frac{7\times 2}{10a^{4}}-\frac{a^{3}}{10a^{4}}}{\frac{3}{11a^{2}}+\frac{7}{33a}}$$

Since \frac{7\times 2}{10a^{4}} and \frac{a^{3}}{10a^{4}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7\times 2-a^{3}}{10a^{4}}}{\frac{3}{11a^{2}}+\frac{7}{33a}}$$

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

$$\frac{\frac{14-a^{3}}{10a^{4}}}{\frac{3}{11a^{2}}+\frac{7}{33a}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 11a^{2} and 33a is 33a^{2}. Multiply \frac{3}{11a^{2}} times \frac{3}{3}. Multiply \frac{7}{33a} times \frac{a}{a}.

$$\frac{\frac{14-a^{3}}{10a^{4}}}{\frac{3\times 3}{33a^{2}}+\frac{7a}{33a^{2}}}$$

Since \frac{3\times 3}{33a^{2}} and \frac{7a}{33a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{14-a^{3}}{10a^{4}}}{\frac{3\times 3+7a}{33a^{2}}}$$

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

$$\frac{\frac{14-a^{3}}{10a^{4}}}{\frac{9+7a}{33a^{2}}}$$

Divide \frac{14-a^{3}}{10a^{4}} by \frac{9+7a}{33a^{2}} by multiplying \frac{14-a^{3}}{10a^{4}} by the reciprocal of \frac{9+7a}{33a^{2}}.

$$\frac{\left(14-a^{3}\right)\times 33a^{2}}{10a^{4}\left(9+7a\right)}$$

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

$$\frac{33\left(-a^{3}+14\right)}{10\left(7a+9\right)a^{2}}$$

Use the distributive property to multiply 33 by -a^{3}+14.

$$\frac{-33a^{3}+462}{10\left(7a+9\right)a^{2}}$$

Use the distributive property to multiply 10 by 7a+9.

$$\frac{-33a^{3}+462}{\left(70a+90\right)a^{2}}$$

Use the distributive property to multiply 70a+90 by a^{2}.

$$\frac{-33a^{3}+462}{70a^{3}+90a^{2}}$$

Expand

$$-\frac{33\left(a^{3}-14\right)}{10\left(7a+9\right)a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5a^{4} and 10a is 10a^{4}. Multiply \frac{7}{5a^{4}} times \frac{2}{2}. Multiply \frac{1}{10a} times \frac{a^{3}}{a^{3}}.

$$\frac{\frac{7\times 2}{10a^{4}}-\frac{a^{3}}{10a^{4}}}{\frac{3}{11a^{2}}+\frac{7}{33a}}$$

Since \frac{7\times 2}{10a^{4}} and \frac{a^{3}}{10a^{4}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7\times 2-a^{3}}{10a^{4}}}{\frac{3}{11a^{2}}+\frac{7}{33a}}$$

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

$$\frac{\frac{14-a^{3}}{10a^{4}}}{\frac{3}{11a^{2}}+\frac{7}{33a}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 11a^{2} and 33a is 33a^{2}. Multiply \frac{3}{11a^{2}} times \frac{3}{3}. Multiply \frac{7}{33a} times \frac{a}{a}.

$$\frac{\frac{14-a^{3}}{10a^{4}}}{\frac{3\times 3}{33a^{2}}+\frac{7a}{33a^{2}}}$$

Since \frac{3\times 3}{33a^{2}} and \frac{7a}{33a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{14-a^{3}}{10a^{4}}}{\frac{3\times 3+7a}{33a^{2}}}$$

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

$$\frac{\frac{14-a^{3}}{10a^{4}}}{\frac{9+7a}{33a^{2}}}$$

Divide \frac{14-a^{3}}{10a^{4}} by \frac{9+7a}{33a^{2}} by multiplying \frac{14-a^{3}}{10a^{4}} by the reciprocal of \frac{9+7a}{33a^{2}}.

$$\frac{\left(14-a^{3}\right)\times 33a^{2}}{10a^{4}\left(9+7a\right)}$$

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

$$\frac{33\left(-a^{3}+14\right)}{10\left(7a+9\right)a^{2}}$$

Use the distributive property to multiply 33 by -a^{3}+14.

$$\frac{-33a^{3}+462}{10\left(7a+9\right)a^{2}}$$

Use the distributive property to multiply 10 by 7a+9.

$$\frac{-33a^{3}+462}{\left(70a+90\right)a^{2}}$$

Use the distributive property to multiply 70a+90 by a^{2}.

$$\frac{-33a^{3}+462}{70a^{3}+90a^{2}}$$