How do you simplify #4/(5n)-1/(10n^3)#?

I'm afraid it can't get much simpler than this.

To simplify the expression 4/(5n) - 1/(10n^3), we need to find a common denominator for the fractions. The least common denominator (LCD) is 10n^3.

Multiplying the first fraction by 2n^2/2n^2 and the second fraction by 1/1, we get:

(8n^2)/(10n^3) - (1)/(10n^3)

Combining the fractions, we have:

(8n^2 - 1)/(10n^3)

Therefore, the simplified expression is (8n^2 - 1)/(10n^3).

To simplify ( \frac{4}{5n} - \frac{1}{10n^3} ), first find a common denominator, which is 10n^3.

Rewrite each fraction with the common denominator:

( \frac{4}{5n} = \frac{4 \times 2n^2}{5n \times 2n^2} = \frac{8n^2}{10n^3} )

( \frac{1}{10n^3} = \frac{1 \times 1}{10n^3 \times 1} = \frac{1}{10n^3} )

Now, subtract the fractions:

( \frac{8n^2}{10n^3} - \frac{1}{10n^3} = \frac{8n^2 - 1}{10n^3} )

Therefore, ( \frac{4}{5n} - \frac{1}{10n^3} ) simplifies to ( \frac{8n^2 - 1}{10n^3} ).