Algebra Examples

$x = \frac{7}{y}$

Step 1

Rewrite the equation as $\frac{7}{y} = x$ .

$\frac{7}{y} = x$

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.

$y, 1$

Step 2.2

The LCM of one and any expression is the expression.

$y$

Step 3

Multiply each term in $\frac{7}{y} = x$ by $y$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{7}{y} = x$ by $y$ .

$\frac{7}{y} y = x y$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $y$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{7}{y} y = x y$

Step 3.2.1.2

Rewrite the expression.

$7 = x y$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $x y = 7$ .

$x y = 7$

Step 4.2

Divide each term in $x y = 7$ by $x$ and simplify.

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Step 4.2.1

Divide each term in $x y = 7$ by $x$ .

$\frac{x y}{x} = \frac{7}{x}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $x$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{x y}{x} = \frac{7}{x}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{7}{x}$

Step 5

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

$f (x) = \frac{7}{x}$