Simplify (3/(3b)-1/(2b))/(2/(3b)+4/(4b))

$\frac{\frac{3}{3 b} - \frac{1}{2 b}}{\frac{2}{3 b} + \frac{4}{4 b}}$

Step 1

Reduce the expression by cancelling the common factors.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\frac{3}{3 b} - \frac{1}{2 b}}{\frac{2}{3 b} + \frac{4}{4 b}}$

Rewrite the expression.

$\frac{\frac{1}{b} - \frac{1}{2 b}}{\frac{2}{3 b} + \frac{4}{4 b}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{\frac{1}{b} - \frac{1}{2 b}}{\frac{2}{3 b} + \frac{4}{4 b}}$

Rewrite the expression.

$\frac{\frac{1}{b} - \frac{1}{2 b}}{\frac{2}{3 b} + \frac{1}{b}}$

Step 2

Multiply the numerator and denominator of the complex fraction by $b \cdot 6$ .

Multiply $\frac{\frac{1}{b} - \frac{1}{2 b}}{\frac{2}{3 b} + \frac{1}{b}}$ by $\frac{b \cdot 6}{b \cdot 6}$ .

$\frac{b \cdot 6}{b \cdot 6} \cdot \frac{\frac{1}{b} - \frac{1}{2 b}}{\frac{2}{3 b} + \frac{1}{b}}$

Combine.

$\frac{b \cdot 6 (\frac{1}{b} - \frac{1}{2 b})}{b \cdot 6 (\frac{2}{3 b} + \frac{1}{b})}$

Step 3

Apply the distributive property.

$\frac{b \cdot 6 \frac{1}{b} + b \cdot 6 (- \frac{1}{2 b})}{b \cdot 6 \frac{2}{3 b} + b \cdot 6 \frac{1}{b}}$

Step 4

Simplify by cancelling.

Cancel the common factor of $b$ .

Factor $b$ out of $b \cdot 6$ .

$\frac{b (6) \frac{1}{b} + b \cdot 6 (- \frac{1}{2 b})}{b \cdot 6 \frac{2}{3 b} + b \cdot 6 \frac{1}{b}}$

Cancel the common factor.

$\frac{b \cdot 6 \frac{1}{b} + b \cdot 6 (- \frac{1}{2 b})}{b \cdot 6 \frac{2}{3 b} + b \cdot 6 \frac{1}{b}}$

Rewrite the expression.

$\frac{6 + b \cdot 6 (- \frac{1}{2 b})}{b \cdot 6 \frac{2}{3 b} + b \cdot 6 \frac{1}{b}}$

Cancel the common factor of $2 b$ .

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

$\frac{6 + b \cdot 6 \frac{- 1}{2 b}}{b \cdot 6 \frac{2}{3 b} + b \cdot 6 \frac{1}{b}}$

Factor $2 b$ out of $b \cdot 6$ .

$\frac{6 + 2 b (3) \frac{- 1}{2 b}}{b \cdot 6 \frac{2}{3 b} + b \cdot 6 \frac{1}{b}}$

Cancel the common factor.

$\frac{6 + 2 b \cdot 3 \frac{- 1}{2 b}}{b \cdot 6 \frac{2}{3 b} + b \cdot 6 \frac{1}{b}}$

Rewrite the expression.

$\frac{6 + 3 \cdot - 1}{b \cdot 6 \frac{2}{3 b} + b \cdot 6 \frac{1}{b}}$

Multiply $3$ by $- 1$ .

$\frac{6 - 3}{b \cdot 6 \frac{2}{3 b} + b \cdot 6 \frac{1}{b}}$

Cancel the common factor of $3 b$ .

Factor $3 b$ out of $b \cdot 6$ .

$\frac{6 - 3}{3 b (2) \frac{2}{3 b} + b \cdot 6 \frac{1}{b}}$

Cancel the common factor.

$\frac{6 - 3}{3 b \cdot 2 \frac{2}{3 b} + b \cdot 6 \frac{1}{b}}$

Rewrite the expression.

$\frac{6 - 3}{2 \cdot 2 + b \cdot 6 \frac{1}{b}}$

Multiply $2$ by $2$ .

$\frac{6 - 3}{4 + b \cdot 6 \frac{1}{b}}$

Cancel the common factor of $b$ .

Factor $b$ out of $b \cdot 6$ .

$\frac{6 - 3}{4 + b (6) \frac{1}{b}}$

Cancel the common factor.

$\frac{6 - 3}{4 + b \cdot 6 \frac{1}{b}}$

Rewrite the expression.

$\frac{6 - 3}{4 + 6}$

Step 5

Simplify by adding and subtracting.

Subtract $3$ from $6$ .

$\frac{3}{4 + 6}$

Add $4$ and $6$ .

$\frac{3}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{10}$

Decimal Form:

$0.3$

Simplify (3/(3b)-1/(2b))/(2/(3b)+4/(4b))

Related Questions

Support LCMGCF.com by disabling your adblocker.