Trigonometry Examples

$\frac{3 x}{x + 3} = 7 - \frac{9}{x + 3}$

Step 1

Simplify $7 - \frac{9}{x + 3}$ .

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Step 1.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

$\frac{3 x}{x + 3} = \frac{7 (x + 3)}{x + 3} - \frac{9}{x + 3}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{3 x}{x + 3} = \frac{7 (x + 3) - 9}{x + 3}$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Apply the distributive property.

$\frac{3 x}{x + 3} = \frac{7 x + 7 \cdot 3 - 9}{x + 3}$

Step 1.3.2

Multiply $7$ by $3$ .

$\frac{3 x}{x + 3} = \frac{7 x + 21 - 9}{x + 3}$

Step 1.3.3

Subtract $9$ from $21$ .

$\frac{3 x}{x + 3} = \frac{7 x + 12}{x + 3}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution

Step 3