Algebra Examples

$y = \frac{3 x}{(x - 3)} \cdot \frac{(x - 4)}{(x + 1)}$

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 $x$ .

$0 = \frac{3 x}{x - 3} \cdot \frac{x - 4}{x + 1}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{3 x}{x - 3} \cdot \frac{x - 4}{x + 1} = 0$ .

$\frac{3 x}{x - 3} \cdot \frac{x - 4}{x + 1} = 0$

Step 1.2.2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$\frac{3 x}{x - 3} = 0$

$\frac{x - 4}{x + 1} = 0$

Step 1.2.3

Set $\frac{3 x}{x - 3}$ equal to $0$ and solve for $x$ .

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Step 1.2.3.1

Set $\frac{3 x}{x - 3}$ equal to $0$ .

$\frac{3 x}{x - 3} = 0$

Step 1.2.3.2

Solve $\frac{3 x}{x - 3} = 0$ for $x$ .

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Step 1.2.3.2.1

Set the numerator equal to zero.

$3 x = 0$

Step 1.2.3.2.2

Divide each term in $3 x = 0$ by $3$ and simplify.

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Step 1.2.3.2.2.1

Divide each term in $3 x = 0$ by $3$ .

$\frac{3 x}{3} = \frac{0}{3}$

Step 1.2.3.2.2.2

Simplify the left side.

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Step 1.2.3.2.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.3.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{0}{3}$

Step 1.2.3.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{3}$

Step 1.2.3.2.2.3

Simplify the right side.

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Step 1.2.3.2.2.3.1

Divide $0$ by $3$ .

$x = 0$

Step 1.2.4

Set $\frac{x - 4}{x + 1}$ equal to $0$ and solve for $x$ .

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Step 1.2.4.1

Set $\frac{x - 4}{x + 1}$ equal to $0$ .

$\frac{x - 4}{x + 1} = 0$

Step 1.2.4.2

Solve $\frac{x - 4}{x + 1} = 0$ for $x$ .

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Step 1.2.4.2.1

Set the numerator equal to zero.

$x - 4 = 0$

Step 1.2.4.2.2

Add $4$ to both sides of the equation.

$x = 4$

Step 1.2.5

The final solution is all the values that make $\frac{3 x}{x - 3} \cdot \frac{x - 4}{x + 1} = 0$ true.

$x = 0, 4$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (4, 0)$

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 $y$ .

$y = \frac{3 (0)}{(0) - 3} \cdot \frac{(0) - 4}{(0) + 1}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \frac{3 (0)}{0 - 3} \cdot \frac{(0) - 4}{(0) + 1}$

Step 2.2.2

Remove parentheses.

$y = \frac{3 (0)}{0 - 3} \cdot \frac{0 - 4}{(0) + 1}$

Step 2.2.3

Remove parentheses.

$y = \frac{3 (0)}{0 - 3} \cdot \frac{0 - 4}{0 + 1}$

Step 2.2.4

Remove parentheses.

$y = \frac{3 (0)}{(0) - 3} \cdot \frac{(0) - 4}{(0) + 1}$

Step 2.2.5

Simplify $\frac{3 (0)}{(0) - 3} \cdot \frac{(0) - 4}{(0) + 1}$ .

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Step 2.2.5.1

Multiply $3$ by $0$ .

$y = \frac{0}{(0) - 3} \cdot \frac{(0) - 4}{(0) + 1}$

Step 2.2.5.2

Subtract $3$ from $0$ .

$y = \frac{0}{- 3} \cdot \frac{(0) - 4}{(0) + 1}$

Step 2.2.5.3

Subtract $4$ from $0$ .

$y = \frac{0}{- 3} \cdot \frac{- 4}{(0) + 1}$

Step 2.2.5.4

Add $0$ and $1$ .

$y = \frac{0}{- 3} \cdot \frac{- 4}{1}$

Step 2.2.5.5

Divide $0$ by $- 3$ .

$y = 0 \cdot \frac{- 4}{1}$

Step 2.2.5.6

Divide $- 4$ by $1$ .

$y = 0 \cdot - 4$

Step 2.2.5.7

Multiply $0$ by $- 4$ .

$y = 0$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 0)$

Step 3

List the intersections.

x-intercept(s): $(0, 0), (4, 0)$

y-intercept(s): $(0, 0)$

Step 4