Precalculus Examples

$2 x - 2 (y d) = y + x d$

Step 1

Subtract $x d$ from both sides of the equation.

$2 x - 2 y d - x d = y$

Step 2

Subtract $2 x$ from both sides of the equation.

$- 2 y d - x d = y - 2 x$

Step 3

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

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Step 3.1

Factor $d$ out of $- 2 y d$ .

$d (- 2 y) - x d = y - 2 x$

Step 3.2

Factor $d$ out of $- x d$ .

$d (- 2 y) + d (- x) = y - 2 x$

Step 3.3

Factor $d$ out of $d (- 2 y) + d (- x)$ .

$d (- 2 y - x) = y - 2 x$

Step 4

Divide each term in $d (- 2 y - x) = y - 2 x$ by $- 2 y - x$ and simplify.

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Step 4.1

Divide each term in $d (- 2 y - x) = y - 2 x$ by $- 2 y - x$ .

$\frac{d (- 2 y - x)}{- 2 y - x} = \frac{y}{- 2 y - x} + \frac{- 2 x}{- 2 y - x}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2 y - x$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{d (- 2 y - x)}{- 2 y - x} = \frac{y}{- 2 y - x} + \frac{- 2 x}{- 2 y - x}$

Step 4.2.1.2

Divide $d$ by $1$ .

$d = \frac{y}{- 2 y - x} + \frac{- 2 x}{- 2 y - x}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Combine the numerators over the common denominator.

$d = \frac{y - 2 x}{- 2 y - x}$

Step 4.3.2

Factor $- 1$ out of $- 2 y$ .

$d = \frac{y - 2 x}{- (2 y) - x}$

Step 4.3.3

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

$d = \frac{y - 2 x}{- (2 y) - (x)}$

Step 4.3.4

Factor $- 1$ out of $- (2 y) - (x)$ .

$d = \frac{y - 2 x}{- (2 y + x)}$

Step 4.3.5

Rewrite negatives.

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Step 4.3.5.1

Rewrite $- (2 y + x)$ as $- 1 (2 y + x)$ .

$d = \frac{y - 2 x}{- 1 (2 y + x)}$

Step 4.3.5.2

Move the negative in front of the fraction.

$d = - \frac{y - 2 x}{2 y + x}$