Calculus Examples

$a = \frac{36}{x} + 6$

Step 1

Rewrite the equation as $\frac{36}{x} + 6 = a$ .

$\frac{36}{x} + 6 = a$

Step 2

Subtract $6$ from both sides of the equation.

$\frac{36}{x} = a - 6$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1, 1$

Step 3.2

The LCM of one and any expression is the expression.

$x$

Step 4

Multiply each term in $\frac{36}{x} = a - 6$ by $x$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{36}{x} = a - 6$ by $x$ .

$\frac{36}{x} x = a x - 6 x$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $x$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{36}{x} x = a x - 6 x$

Step 4.2.1.2

Rewrite the expression.

$36 = a x - 6 x$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $a x - 6 x = 36$ .

$a x - 6 x = 36$

Step 5.2

Factor $x$ out of $a x - 6 x$ .

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Step 5.2.1

Factor $x$ out of $a x$ .

$x a - 6 x = 36$

Step 5.2.2

Factor $x$ out of $- 6 x$ .

$x a + x \cdot - 6 = 36$

Step 5.2.3

Factor $x$ out of $x a + x \cdot - 6$ .

$x (a - 6) = 36$

Step 5.3

Divide each term in $x (a - 6) = 36$ by $a - 6$ and simplify.

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Step 5.3.1

Divide each term in $x (a - 6) = 36$ by $a - 6$ .

$\frac{x (a - 6)}{a - 6} = \frac{36}{a - 6}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $a - 6$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{x (a - 6)}{a - 6} = \frac{36}{a - 6}$

Step 5.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{36}{a - 6}$