Solve a/8-4/a^2/4

$$\frac { \frac { a } { 8 } - \frac { 4 } { a ^ { 2 } } } { 4 }$$

Evaluate

$$\frac{a}{32}-\frac{1}{a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and a^{2} is 8a^{2}. Multiply \frac{a}{8} times \frac{a^{2}}{a^{2}}. Multiply \frac{4}{a^{2}} times \frac{8}{8}.

$$\frac{\frac{aa^{2}}{8a^{2}}-\frac{4\times 8}{8a^{2}}}{4}$$

Since \frac{aa^{2}}{8a^{2}} and \frac{4\times 8}{8a^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{aa^{2}-4\times 8}{8a^{2}}}{4}$$

Do the multiplications in aa^{2}-4\times 8.

$$\frac{\frac{a^{3}-32}{8a^{2}}}{4}$$

Express \frac{\frac{a^{3}-32}{8a^{2}}}{4} as a single fraction.

$$\frac{a^{3}-32}{8a^{2}\times 4}$$

Multiply 8 and 4 to get 32.

$$\frac{a^{3}-32}{32a^{2}}$$

Expand

$$\frac{a}{32}-\frac{1}{a^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and a^{2} is 8a^{2}. Multiply \frac{a}{8} times \frac{a^{2}}{a^{2}}. Multiply \frac{4}{a^{2}} times \frac{8}{8}.

$$\frac{\frac{aa^{2}}{8a^{2}}-\frac{4\times 8}{8a^{2}}}{4}$$

Since \frac{aa^{2}}{8a^{2}} and \frac{4\times 8}{8a^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{aa^{2}-4\times 8}{8a^{2}}}{4}$$

Do the multiplications in aa^{2}-4\times 8.

$$\frac{\frac{a^{3}-32}{8a^{2}}}{4}$$

Express \frac{\frac{a^{3}-32}{8a^{2}}}{4} as a single fraction.

$$\frac{a^{3}-32}{8a^{2}\times 4}$$

Multiply 8 and 4 to get 32.

$$\frac{a^{3}-32}{32a^{2}}$$