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

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

Multiply the numerator and denominator of the complex fraction by $4 y$ .

Multiply $\frac{\frac{3}{4 y} - \frac{2}{y}}{\frac{1}{y} + \frac{3}{2 y}}$ by $\frac{4 y}{4 y}$ .

$\frac{4 y}{4 y} \cdot \frac{\frac{3}{4 y} - \frac{2}{y}}{\frac{1}{y} + \frac{3}{2 y}}$

Combine.

$\frac{4 y (\frac{3}{4 y} - \frac{2}{y})}{4 y (\frac{1}{y} + \frac{3}{2 y})}$

Apply the distributive property.

$\frac{4 y \frac{3}{4 y} + 4 y (- \frac{2}{y})}{4 y \frac{1}{y} + 4 y \frac{3}{2 y}}$

Simplify by cancelling.

Cancel the common factor of $4 y$ .

Cancel the common factor.

$\frac{4 y \frac{3}{4 y} + 4 y (- \frac{2}{y})}{4 y \frac{1}{y} + 4 y \frac{3}{2 y}}$

Rewrite the expression.

$\frac{3 + 4 y (- \frac{2}{y})}{4 y \frac{1}{y} + 4 y \frac{3}{2 y}}$

Cancel the common factor of $y$ .

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

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

Factor $y$ out of $4 y$ .

$\frac{3 + y \cdot 4 \frac{- 2}{y}}{4 y \frac{1}{y} + 4 y \frac{3}{2 y}}$

Cancel the common factor.

$\frac{3 + y \cdot 4 \frac{- 2}{y}}{4 y \frac{1}{y} + 4 y \frac{3}{2 y}}$

Rewrite the expression.

$\frac{3 + 4 \cdot - 2}{4 y \frac{1}{y} + 4 y \frac{3}{2 y}}$

Multiply $4$ by $- 2$ .

$\frac{3 - 8}{4 y \frac{1}{y} + 4 y \frac{3}{2 y}}$

Cancel the common factor of $y$ .

Factor $y$ out of $4 y$ .

$\frac{3 - 8}{y \cdot 4 \frac{1}{y} + 4 y \frac{3}{2 y}}$

Cancel the common factor.

$\frac{3 - 8}{y \cdot 4 \frac{1}{y} + 4 y \frac{3}{2 y}}$

Rewrite the expression.

$\frac{3 - 8}{4 + 4 y \frac{3}{2 y}}$

Cancel the common factor of $2 y$ .

Factor $2 y$ out of $4 y$ .

$\frac{3 - 8}{4 + 2 y (2) \frac{3}{2 y}}$

Cancel the common factor.

$\frac{3 - 8}{4 + 2 y \cdot 2 \frac{3}{2 y}}$

Rewrite the expression.

$\frac{3 - 8}{4 + 2 \cdot 3}$

Multiply $2$ by $3$ .

$\frac{3 - 8}{4 + 6}$

Reduce the expression by cancelling the common factors.

Subtract $8$ from $3$ .

$\frac{- 5}{4 + 6}$

Add $4$ and $6$ .

$\frac{- 5}{10}$

Cancel the common factor of $- 5$ and $10$ .

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{5 \cdot - 1}{5 \cdot 2}$

Cancel the common factor.

$\frac{5 \cdot - 1}{5 \cdot 2}$

Rewrite the expression.

$\frac{- 1}{2}$

Move the negative in front of the fraction.

$- \frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$

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

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