Trigonometry Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $2 d$ .

Tap for more steps...

Step 1.1

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

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Tap for more steps...

Step 3.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $2 d$ .

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

Step 3.1.2

Cancel the common factor.

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

Step 3.1.3

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $d$ .

Tap for more steps...

Step 3.2.1

Move the leading negative in $- \frac{4}{d}$ into the numerator.

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

Step 3.2.2

Factor $d$ out of $2 d$ .

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

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

Step 3.3

Multiply $2$ by $- 4$ .

$\frac{d - 8}{2 d \frac{1}{d} + 2 d \frac{3}{2 d}}$

Step 3.4

Cancel the common factor of $d$ .

Tap for more steps...

Step 3.4.1

Factor $d$ out of $2 d$ .

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

Step 3.4.2

Cancel the common factor.

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

Step 3.4.3

Rewrite the expression.

$\frac{d - 8}{2 + 2 d \frac{3}{2 d}}$

Step 3.5

Cancel the common factor of $2 d$ .

Tap for more steps...

Step 3.5.1

Cancel the common factor.

$\frac{d - 8}{2 + 2 d \frac{3}{2 d}}$

Step 3.5.2

Rewrite the expression.

$\frac{d - 8}{2 + 3}$

Step 4

Add $2$ and $3$ .

$\frac{d - 8}{5}$