Precalculus Examples

$f (x) = \frac{X + 8}{6 x - 15}$

Step 1

Subtract $\frac{X + 8}{6 x - 15}$ from both sides of the equation.

$y - \frac{X + 8}{6 x - 15} = 0$

Step 2

Factor $3$ out of $6 x - 15$ .

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Step 2.1

Factor $3$ out of $6 x$ .

$y - \frac{X + 8}{3 (2 x) - 15} = 0$

Step 2.2

Factor $3$ out of $- 15$ .

$y - \frac{X + 8}{3 (2 x) + 3 (- 5)} = 0$

Step 2.3

Factor $3$ out of $3 (2 x) + 3 (- 5)$ .

$y - \frac{X + 8}{3 (2 x - 5)} = 0$

Step 3

To write $y$ as a fraction with a common denominator, multiply by $\frac{3 (2 x - 5)}{3 (2 x - 5)}$ .

$y \cdot \frac{3 (2 x - 5)}{3 (2 x - 5)} - \frac{X + 8}{3 (2 x - 5)} = 0$

Step 4

Combine $y$ and $\frac{3 (2 x - 5)}{3 (2 x - 5)}$ .

$\frac{y (3 (2 x - 5))}{3 (2 x - 5)} - \frac{X + 8}{3 (2 x - 5)} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{y (3 (2 x - 5)) - (X + 8)}{3 (2 x - 5)} = 0$

Step 6

Simplify the numerator.

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Step 6.1

Move $3$ to the left of $y$ .

$\frac{3 \cdot y (2 x - 5) - (X + 8)}{3 (2 x - 5)} = 0$

Step 6.2

Apply the distributive property.

$\frac{3 y (2 x) + 3 y \cdot - 5 - (X + 8)}{3 (2 x - 5)} = 0$

Step 6.3

Rewrite using the commutative property of multiplication.

$\frac{3 \cdot 2 y x + 3 y \cdot - 5 - (X + 8)}{3 (2 x - 5)} = 0$

Step 6.4

Multiply $- 5$ by $3$ .

$\frac{3 \cdot 2 y x - 15 y - (X + 8)}{3 (2 x - 5)} = 0$

Step 6.5

Multiply $3$ by $2$ .

$\frac{6 y x - 15 y - (X + 8)}{3 (2 x - 5)} = 0$

Step 6.6

Apply the distributive property.

$\frac{6 y x - 15 y - X - 1 \cdot 8}{3 (2 x - 5)} = 0$

Step 6.7

Multiply $- 1$ by $8$ .

$\frac{6 y x - 15 y - X - 8}{3 (2 x - 5)} = 0$