Algebra Examples

$y = \frac{5}{6 x - 72}$

Rewrite the equation as $\frac{5}{6 x - 72} = y$ .

$\frac{5}{6 x - 72} = y$

Factor $6$ out of $6 x - 72$ .

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Factor $6$ out of $6 x$ .

$\frac{5}{6 (x) - 72} = y$

Factor $6$ out of $- 72$ .

$\frac{5}{6 x + 6 \cdot - 12} = y$

Factor $6$ out of $6 x + 6 \cdot - 12$ .

$\frac{5}{6 (x - 12)} = y$

Find the LCD of the terms in the equation.

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

$6 (x - 12), 1$

The LCM of one and any expression is the expression.

$6 (x - 12)$

Multiply each term in $\frac{5}{6 (x - 12)} = y$ by $6 (x - 12)$ to eliminate the fractions.

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Multiply each term in $\frac{5}{6 (x - 12)} = y$ by $6 (x - 12)$ .

$\frac{5}{6 (x - 12)} (6 (x - 12)) = y (6 (x - 12))$

Simplify the left side.

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Rewrite using the commutative property of multiplication.

$6 \frac{5}{6 (x - 12)} (x - 12) = y (6 (x - 12))$

Cancel the common factor of $6$ .

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Cancel the common factor.

$6 \frac{5}{6 (x - 12)} (x - 12) = y (6 (x - 12))$

Rewrite the expression.

$\frac{5}{x - 12} (x - 12) = y (6 (x - 12))$

Cancel the common factor of $x - 12$ .

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Cancel the common factor.

$\frac{5}{x - 12} (x - 12) = y (6 (x - 12))$

Rewrite the expression.

$5 = y (6 (x - 12))$

Simplify the right side.

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Rewrite using the commutative property of multiplication.

$5 = 6 y (x - 12)$

Apply the distributive property.

$5 = 6 y x + 6 y \cdot - 12$

Multiply $- 12$ by $6$ .

$5 = 6 y x - 72 y$

Solve the equation.

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Rewrite the equation as $6 y x - 72 y = 5$ .

$6 y x - 72 y = 5$

Add $72 y$ to both sides of the equation.

$6 y x = 5 + 72 y$

Divide each term in $6 y x = 5 + 72 y$ by $6 y$ and simplify.

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Divide each term in $6 y x = 5 + 72 y$ by $6 y$ .

$\frac{6 y x}{6 y} = \frac{5}{6 y} + \frac{72 y}{6 y}$

Simplify the left side.

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Cancel the common factor of $6$ .

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Cancel the common factor.

$\frac{6 y x}{6 y} = \frac{5}{6 y} + \frac{72 y}{6 y}$

Rewrite the expression.

$\frac{y x}{y} = \frac{5}{6 y} + \frac{72 y}{6 y}$

Cancel the common factor of $y$ .

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Cancel the common factor.

$\frac{y x}{y} = \frac{5}{6 y} + \frac{72 y}{6 y}$

Divide $x$ by $1$ .

$x = \frac{5}{6 y} + \frac{72 y}{6 y}$

Simplify the right side.

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Simplify each term.

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Cancel the common factor of $72$ and $6$ .

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Factor $6$ out of $72 y$ .

$x = \frac{5}{6 y} + \frac{6 (12 y)}{6 y}$

Cancel the common factors.

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Factor $6$ out of $6 y$ .

$x = \frac{5}{6 y} + \frac{6 (12 y)}{6 (y)}$

Cancel the common factor.

$x = \frac{5}{6 y} + \frac{6 (12 y)}{6 y}$

Rewrite the expression.

$x = \frac{5}{6 y} + \frac{12 y}{y}$

Cancel the common factor of $y$ .

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Cancel the common factor.

$x = \frac{5}{6 y} + \frac{12 y}{y}$

Divide $12$ by $1$ .

$x = \frac{5}{6 y} + 12$

To rewrite as a function of $y$ , write the equation so that $x$ is by itself on one side of the equal sign and an expression involving only $y$ is on the other side.

$f (y) = \frac{5}{6 y} + 12$