Precalculus Examples

$- 3 y + x y = - 5 x$

Step 1

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

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Step 1.1

Factor $y$ out of $- 3 y$ .

$y \cdot - 3 + x y = - 5 x$

Step 1.2

Factor $y$ out of $x y$ .

$y \cdot - 3 + y x = - 5 x$

Step 1.3

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

$y (- 3 + x) = - 5 x$

Step 2

Divide each term in $y (- 3 + x) = - 5 x$ by $- 3 + x$ and simplify.

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Step 2.1

Divide each term in $y (- 3 + x) = - 5 x$ by $- 3 + x$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 3 + x$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $y$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

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

Step 2.3.2

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

$y = - \frac{5 x}{- 1 (3) + x}$

Step 2.3.3

Factor $- 1$ out of $x$ .

$y = - \frac{5 x}{- 1 (3) - 1 (- x)}$

Step 2.3.4

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

$y = - \frac{5 x}{- 1 (3 - x)}$

Step 2.3.5

Simplify the expression.

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Step 2.3.5.1

Move the negative in front of the fraction.

$y = - - \frac{5 x}{3 - x}$

Step 2.3.5.2

Multiply $- 1$ by $- 1$ .

$y = 1 \frac{5 x}{3 - x}$

Step 2.3.5.3

Multiply $\frac{5 x}{3 - x}$ by $1$ .

$y = \frac{5 x}{3 - x}$