Algebra Examples

$y = - 12 + \frac{4}{x}$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - 12 + \frac{4}{x}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- 12 + \frac{4}{x} = 0$ .

$- 12 + \frac{4}{x} = 0$

Step 1.2.2

Add $12$ to both sides of the equation.

$\frac{4}{x} = 12$

Step 1.2.3

Find the LCD of the terms in the equation.

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Step 1.2.3.1

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

$x, 1$

Step 1.2.3.2

The LCM of one and any expression is the expression.

$x$

Step 1.2.4

Multiply each term in $\frac{4}{x} = 12$ by $x$ to eliminate the fractions.

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Step 1.2.4.1

Multiply each term in $\frac{4}{x} = 12$ by $x$ .

$\frac{4}{x} x = 12 x$

Step 1.2.4.2

Simplify the left side.

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Step 1.2.4.2.1

Cancel the common factor of $x$ .

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Step 1.2.4.2.1.1

Cancel the common factor.

$\frac{4}{x} x = 12 x$

Step 1.2.4.2.1.2

Rewrite the expression.

$4 = 12 x$

Step 1.2.5

Solve the equation.

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Step 1.2.5.1

Rewrite the equation as $12 x = 4$ .

$12 x = 4$

Step 1.2.5.2

Divide each term in $12 x = 4$ by $12$ and simplify.

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Step 1.2.5.2.1

Divide each term in $12 x = 4$ by $12$ .

$\frac{12 x}{12} = \frac{4}{12}$

Step 1.2.5.2.2

Simplify the left side.

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Step 1.2.5.2.2.1

Cancel the common factor of $12$ .

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Step 1.2.5.2.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{4}{12}$

Step 1.2.5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{12}$

Step 1.2.5.2.3

Simplify the right side.

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Step 1.2.5.2.3.1

Cancel the common factor of $4$ and $12$ .

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Step 1.2.5.2.3.1.1

Factor $4$ out of $4$ .

$x = \frac{4 (1)}{12}$

Step 1.2.5.2.3.1.2

Cancel the common factors.

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Step 1.2.5.2.3.1.2.1

Factor $4$ out of $12$ .

$x = \frac{4 \cdot 1}{4 \cdot 3}$

Step 1.2.5.2.3.1.2.2

Cancel the common factor.

$x = \frac{4 \cdot 1}{4 \cdot 3}$

Step 1.2.5.2.3.1.2.3

Rewrite the expression.

$x = \frac{1}{3}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{3}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - 12 + \frac{4}{0}$

Step 2.2

The equation has an undefined fraction.

Undefined

Step 2.3

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(\frac{1}{3}, 0)$

y-intercept(s): $None$

Step 4