Simplify (2/(3m)-1/(2m))/(3/(3m)+4/(5m))

$\frac{\frac{2}{3 m} - \frac{1}{2 m}}{\frac{3}{3 m} + \frac{4}{5 m}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\frac{2}{3 m} - \frac{1}{2 m}}{\frac{3}{3 m} + \frac{4}{5 m}}$

Rewrite the expression.

$\frac{\frac{2}{3 m} - \frac{1}{2 m}}{\frac{1}{m} + \frac{4}{5 m}}$

Multiply the numerator and denominator of the complex fraction by $30 m$ .

Multiply $\frac{\frac{2}{3 m} - \frac{1}{2 m}}{\frac{1}{m} + \frac{4}{5 m}}$ by $\frac{30 m}{30 m}$ .

$\frac{30 m}{30 m} \cdot \frac{\frac{2}{3 m} - \frac{1}{2 m}}{\frac{1}{m} + \frac{4}{5 m}}$

Combine.

$\frac{30 m (\frac{2}{3 m} - \frac{1}{2 m})}{30 m (\frac{1}{m} + \frac{4}{5 m})}$

Apply the distributive property.

$\frac{30 m \frac{2}{3 m} + 30 m (- \frac{1}{2 m})}{30 m \frac{1}{m} + 30 m \frac{4}{5 m}}$

Simplify by cancelling.

Cancel the common factor of $3 m$ .

Factor $3 m$ out of $30 m$ .

$\frac{3 m (10) \frac{2}{3 m} + 30 m (- \frac{1}{2 m})}{30 m \frac{1}{m} + 30 m \frac{4}{5 m}}$

Cancel the common factor.

$\frac{3 m \cdot 10 \frac{2}{3 m} + 30 m (- \frac{1}{2 m})}{30 m \frac{1}{m} + 30 m \frac{4}{5 m}}$

Rewrite the expression.

$\frac{10 \cdot 2 + 30 m (- \frac{1}{2 m})}{30 m \frac{1}{m} + 30 m \frac{4}{5 m}}$

Multiply $10$ by $2$ .

$\frac{20 + 30 m (- \frac{1}{2 m})}{30 m \frac{1}{m} + 30 m \frac{4}{5 m}}$

Cancel the common factor of $2 m$ .

Move the leading negative in $- \frac{1}{2 m}$ into the numerator.

$\frac{20 + 30 m \frac{- 1}{2 m}}{30 m \frac{1}{m} + 30 m \frac{4}{5 m}}$

Factor $2 m$ out of $30 m$ .

$\frac{20 + 2 m (15) \frac{- 1}{2 m}}{30 m \frac{1}{m} + 30 m \frac{4}{5 m}}$

Cancel the common factor.

$\frac{20 + 2 m \cdot 15 \frac{- 1}{2 m}}{30 m \frac{1}{m} + 30 m \frac{4}{5 m}}$

Rewrite the expression.

$\frac{20 + 15 \cdot - 1}{30 m \frac{1}{m} + 30 m \frac{4}{5 m}}$

Multiply $15$ by $- 1$ .

$\frac{20 - 15}{30 m \frac{1}{m} + 30 m \frac{4}{5 m}}$

Cancel the common factor of $m$ .

Factor $m$ out of $30 m$ .

$\frac{20 - 15}{m \cdot 30 \frac{1}{m} + 30 m \frac{4}{5 m}}$

Cancel the common factor.

$\frac{20 - 15}{m \cdot 30 \frac{1}{m} + 30 m \frac{4}{5 m}}$

Rewrite the expression.

$\frac{20 - 15}{30 + 30 m \frac{4}{5 m}}$

Cancel the common factor of $5 m$ .

Factor $5 m$ out of $30 m$ .

$\frac{20 - 15}{30 + 5 m (6) \frac{4}{5 m}}$

Cancel the common factor.

$\frac{20 - 15}{30 + 5 m \cdot 6 \frac{4}{5 m}}$

Rewrite the expression.

$\frac{20 - 15}{30 + 6 \cdot 4}$

Multiply $6$ by $4$ .

$\frac{20 - 15}{30 + 24}$

Simplify by adding and subtracting.

Subtract $15$ from $20$ .

$\frac{5}{30 + 24}$

Add $30$ and $24$ .

$\frac{5}{54}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{54}$

Decimal Form:

$0.0\overline{925}$

Simplify (2/(3m)-1/(2m))/(3/(3m)+4/(5m))

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