Trigonometry Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $2 - x$ .

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Step 1.1

Multiply $\frac{\frac{2 (4 x - 3)}{2 - x} + 3}{\frac{4 x - 3}{2 - x} + 4}$ by $\frac{2 - x}{2 - x}$ .

$\frac{2 - x}{2 - x} \cdot \frac{\frac{2 (4 x - 3)}{2 - x} + 3}{\frac{4 x - 3}{2 - x} + 4}$

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

$\frac{(2 - x) \frac{2 (4 x - 3)}{2 - x} + (2 - x) \cdot 3}{(2 - x) \frac{4 x - 3}{2 - x} + (2 - x) \cdot 4}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $2 - x$ .

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Step 3.1.1

Cancel the common factor.

$\frac{(2 - x) \frac{2 (4 x - 3)}{2 - x} + (2 - x) \cdot 3}{(2 - x) \frac{4 x - 3}{2 - x} + (2 - x) \cdot 4}$

Step 3.1.2

Rewrite the expression.

$\frac{2 (4 x - 3) + (2 - x) \cdot 3}{(2 - x) \frac{4 x - 3}{2 - x} + (2 - x) \cdot 4}$

Step 3.2

Cancel the common factor of $2 - x$ .

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Step 3.2.1

Cancel the common factor.

$\frac{2 (4 x - 3) + (2 - x) \cdot 3}{(2 - x) \frac{4 x - 3}{2 - x} + (2 - x) \cdot 4}$

Step 3.2.2

Rewrite the expression.

$\frac{2 (4 x - 3) + (2 - x) \cdot 3}{4 x - 3 + (2 - x) \cdot 4}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{2 (4 x) + 2 \cdot - 3 + (2 - x) \cdot 3}{4 x - 3 + (2 - x) \cdot 4}$

Step 4.2

Multiply $4$ by $2$ .

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

Step 4.3

Multiply $2$ by $- 3$ .

$\frac{8 x - 6 + (2 - x) \cdot 3}{4 x - 3 + (2 - x) \cdot 4}$

Step 4.4

Apply the distributive property.

$\frac{8 x - 6 + 2 \cdot 3 - x \cdot 3}{4 x - 3 + (2 - x) \cdot 4}$

Step 4.5

Multiply $2$ by $3$ .

$\frac{8 x - 6 + 6 - x \cdot 3}{4 x - 3 + (2 - x) \cdot 4}$

Step 4.6

Multiply $3$ by $- 1$ .

$\frac{8 x - 6 + 6 - 3 x}{4 x - 3 + (2 - x) \cdot 4}$

Step 4.7

Subtract $3 x$ from $8 x$ .

$\frac{5 x - 6 + 6}{4 x - 3 + (2 - x) \cdot 4}$

Step 4.8

Add $- 6$ and $6$ .

$\frac{5 x + 0}{4 x - 3 + (2 - x) \cdot 4}$

Step 4.9

Add $5 x$ and $0$ .

$\frac{5 x}{4 x - 3 + (2 - x) \cdot 4}$

Step 5

Simplify the denominator.

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Step 5.1

Apply the distributive property.

$\frac{5 x}{4 x - 3 + 2 \cdot 4 - x \cdot 4}$

Step 5.2

Multiply $2$ by $4$ .

$\frac{5 x}{4 x - 3 + 8 - x \cdot 4}$

Step 5.3

Multiply $4$ by $- 1$ .

$\frac{5 x}{4 x - 3 + 8 - 4 x}$

Step 5.4

Subtract $4 x$ from $4 x$ .

$\frac{5 x}{0 - 3 + 8}$

Step 5.5

Subtract $3$ from $0$ .

$\frac{5 x}{- 3 + 8}$

Step 5.6

Add $- 3$ and $8$ .

$\frac{5 x}{5}$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Cancel the common factor.

$\frac{5 x}{5}$

Step 6.2

Divide $x$ by $1$ .

$x$