Precalculus Examples

$x = \frac{km}{y - z}$

Step 1

Rewrite the equation as $\frac{km}{y - z} = x$ .

$\frac{km}{y - z} = x$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

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

$y - z, 1$

Step 2.2

Remove parentheses.

$y - z, 1$

Step 2.3

The LCM of one and any expression is the expression.

$y - z$

Step 3

Multiply each term in $\frac{km}{y - z} = x$ by $y - z$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{km}{y - z} = x$ by $y - z$ .

$\frac{km}{y - z} (y - z) = x (y - z)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $y - z$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{km}{y - z} (y - z) = x (y - z)$

Step 3.2.1.2

Rewrite the expression.

$km = x (y - z)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$km = x y + x (- z)$

Step 3.3.2

Rewrite using the commutative property of multiplication.

$km = x y - x z$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $x y - x z = km$ .

$x y - x z = km$

Step 4.2

Add $x z$ to both sides of the equation.

$x y = km + x z$

Step 4.3

Divide each term in $x y = km + x z$ by $x$ and simplify.

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Step 4.3.1

Divide each term in $x y = km + x z$ by $x$ .

$\frac{x y}{x} = \frac{km}{x} + \frac{x z}{x}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $x$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{x y}{x} = \frac{km}{x} + \frac{x z}{x}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{km}{x} + \frac{x z}{x}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $x$ .

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Step 4.3.3.1.1

Cancel the common factor.

$y = \frac{km}{x} + \frac{x z}{x}$

Step 4.3.3.1.2

Divide $z$ by $1$ .

$y = \frac{km}{x} + z$

Step 5

Rewrite the expression.

$y = \frac{1}{x} km + z$