Calculus Examples

$x + a = \frac{b}{3} \cdot x$

Step 1

Simplify $\frac{b}{3} \cdot x$ .

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Step 1.1

Rewrite.

$x + a = 0 + 0 + \frac{b}{3} \cdot x$

Step 1.2

Simplify by adding zeros.

$x + a = \frac{b}{3} \cdot x$

Step 1.3

Combine $\frac{b}{3}$ and $x$ .

$x + a = \frac{b x}{3}$

Step 2

Subtract $\frac{b x}{3}$ from both sides of the equation.

$x + a - \frac{b x}{3} = 0$

Step 3

Subtract $a$ from both sides of the equation.

$x - \frac{b x}{3} = - a$

Step 4

Factor $x$ out of $x - \frac{b x}{3}$ .

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Step 4.1

Factor $x$ out of $x^{1}$ .

$x \cdot 1 - \frac{b x}{3} = - a$

Step 4.2

Factor $x$ out of $- \frac{b x}{3}$ .

$x \cdot 1 + x (- \frac{b}{3}) = - a$

Step 4.3

Factor $x$ out of $x \cdot 1 + x (- \frac{b}{3})$ .

$x (1 - \frac{b}{3}) = - a$

Step 5

Divide each term in $x (1 - \frac{b}{3}) = - a$ by $1 - \frac{b}{3}$ and simplify.

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Step 5.1

Divide each term in $x (1 - \frac{b}{3}) = - a$ by $1 - \frac{b}{3}$ .

$\frac{x (1 - \frac{b}{3})}{1 - \frac{b}{3}} = \frac{- a}{1 - \frac{b}{3}}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $1 - \frac{b}{3}$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x (1 - \frac{b}{3})}{1 - \frac{b}{3}} = \frac{- a}{1 - \frac{b}{3}}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- a}{1 - \frac{b}{3}}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify the denominator.

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Step 5.3.1.1

Write $1$ as a fraction with a common denominator.

$x = \frac{- a}{\frac{3}{3} - \frac{b}{3}}$

Step 5.3.1.2

Combine the numerators over the common denominator.

$x = \frac{- a}{\frac{3 - b}{3}}$

Step 5.3.2

Multiply the numerator by the reciprocal of the denominator.

$x = - a \frac{3}{3 - b}$

Step 5.3.3

Combine $\frac{3}{3 - b}$ and $a$ .

$x = - \frac{3 a}{3 - b}$