Pre-Algebra Examples

$y = \frac{5 x - 12}{- 3 x + 15}$

Step 1

Simplify $\frac{5 x - 12}{- 3 x + 15}$ .

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Step 1.1

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

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Step 1.1.1

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

$y = \frac{5 x - 12}{3 (- x) + 15}$

Step 1.1.2

Factor $3$ out of $15$ .

$y = \frac{5 x - 12}{3 (- x) + 3 (5)}$

Step 1.1.3

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

$y = \frac{5 x - 12}{3 (- x + 5)}$

Step 1.2

Split the fraction $\frac{5 x - 12}{3 (- x + 5)}$ into two fractions.

$y = \frac{5 x}{3 (- x + 5)} + \frac{- 12}{3 (- x + 5)}$

Step 1.3

Simplify each term.

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Step 1.3.1

Cancel the common factor of $- 12$ and $3$ .

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Step 1.3.1.1

Factor $3$ out of $- 12$ .

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

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Cancel the common factor.

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

Step 1.3.1.2.2

Rewrite the expression.

$y = \frac{5 x}{3 (- x + 5)} + \frac{- 4}{- x + 5}$

Step 1.3.2

Move the negative in front of the fraction.

$y = \frac{5 x}{3 (- x + 5)} - \frac{4}{- x + 5}$

Step 2

To write $- \frac{4}{- x + 5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

Write each expression with a common denominator of $3 (- x + 5)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4}{- x + 5}$ by $\frac{3}{3}$ .

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

Step 3.2

Reorder the factors of $(- x + 5) \cdot 3$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Multiply $- 4$ by $3$ .

$y = \frac{5 x - 12}{3 (- x + 5)}$

Step 6

The given equation $y = \frac{5 x - 12}{3 (- x + 5)}$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$