Calculus Examples

$y + x \cdot \tan (y) = x$

Step 1

Subtract $x$ from both sides of the equation.

$y + x \cdot \tan (y) - x = 0$

Step 2

Subtract $y$ from both sides of the equation.

$x \cdot \tan (y) - x = - y$

Step 3

Factor $x$ out of $x \cdot \tan (y) - x$ .

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Step 3.1

Factor $x$ out of $x \cdot \tan (y)$ .

$x (\tan (y)) - x = - y$

Step 3.2

Factor $x$ out of $- x$ .

$x (\tan (y)) + x \cdot - 1 = - y$

Step 3.3

Factor $x$ out of $x (\tan (y)) + x \cdot - 1$ .

$x (\tan (y) - 1) = - y$

Step 4

Divide each term in $x (\tan (y) - 1) = - y$ by $\tan (y) - 1$ and simplify.

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Step 4.1

Divide each term in $x (\tan (y) - 1) = - y$ by $\tan (y) - 1$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $\tan (y) - 1$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

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