Trigonometry Examples

$\frac{3 x}{2 x - 6} + \frac{9}{6 - 2 x}$

Step 1

Simplify terms.

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Step 1.1

Simplify each term.

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Step 1.1.1

Factor $2$ out of $2 x - 6$ .

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Step 1.1.1.1

Factor $2$ out of $2 x$ .

$\frac{3 x}{2 (x) - 6} + \frac{9}{6 - 2 x}$

Step 1.1.1.2

Factor $2$ out of $- 6$ .

$\frac{3 x}{2 x + 2 \cdot - 3} + \frac{9}{6 - 2 x}$

Step 1.1.1.3

Factor $2$ out of $2 x + 2 \cdot - 3$ .

$\frac{3 x}{2 (x - 3)} + \frac{9}{6 - 2 x}$

Step 1.1.2

Factor $2$ out of $6 - 2 x$ .

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Step 1.1.2.1

Factor $2$ out of $6$ .

$\frac{3 x}{2 (x - 3)} + \frac{9}{2 (3) - 2 x}$

Step 1.1.2.2

Factor $2$ out of $- 2 x$ .

$\frac{3 x}{2 (x - 3)} + \frac{9}{2 (3) + 2 (- x)}$

Step 1.1.2.3

Factor $2$ out of $2 (3) + 2 (- x)$ .

$\frac{3 x}{2 (x - 3)} + \frac{9}{2 (3 - x)}$

Step 1.2

Simplify terms.

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Step 1.2.1

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{3 x}{2 (x - 3)} + \frac{9}{2 (- 1 (- 3) - x)}$

Step 1.2.2

Factor $- 1$ out of $- x$ .

$\frac{3 x}{2 (x - 3)} + \frac{9}{2 (- 1 (- 3) - (x))}$

Step 1.2.3

Factor $- 1$ out of $- 1 (- 3) - (x)$ .

$\frac{3 x}{2 (x - 3)} + \frac{9}{2 (- 1 (- 3 + x))}$

Step 1.2.4

Simplify the expression.

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Step 1.2.4.1

Move a negative from the denominator of $\frac{9}{2 (- 1 (- 3 + x))}$ to the numerator.

$\frac{3 x}{2 (x - 3)} + \frac{- 1 \cdot 9}{2 (- 3 + x)}$

Step 1.2.4.2

Reorder terms.

$\frac{3 x}{2 (x - 3)} + \frac{- 1 \cdot 9}{2 (x - 3)}$

Step 1.2.5

Combine the numerators over the common denominator.

$\frac{3 x - 1 \cdot 9}{2 (x - 3)}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 1$ by $9$ .

$\frac{3 x - 9}{2 (x - 3)}$

Step 2.2

Factor $3$ out of $3 x - 9$ .

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Step 2.2.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 9}{2 (x - 3)}$

Step 2.2.2

Factor $3$ out of $- 9$ .

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

Step 2.2.3

Factor $3$ out of $3 x + 3 \cdot - 3$ .

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

Step 3

Cancel the common factor of $x - 3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$