Find the x and y Intercepts (5x)/(2x-5)

$\frac{5 x}{2 x - 5}$

Step 1

Write $\frac{5 x}{2 x - 5}$ as an equation.

$y = \frac{5 x}{2 x - 5}$

Step 2

Find the x-intercepts.

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

$0 = \frac{5 x}{2 x - 5}$

Solve the equation.

Set the numerator equal to zero.

$5 x = 0$

Divide each term in $5 x = 0$ by $5$ and simplify.

Divide each term in $5 x = 0$ by $5$ .

$\frac{5 x}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{0}{5}$

Divide $x$ by $1$ .

$x = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$x = 0$

x-intercept(s) in point form.

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

Step 3

Find the y-intercepts.

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

$y = \frac{5 (0)}{2 (0) - 5}$

Solve the equation.

Remove parentheses.

$y = \frac{5 (0)}{2 (0) - 5}$

Simplify $\frac{5 (0)}{2 (0) - 5}$ .

Cancel the common factors.

Factor $5$ out of $2 (0)$ .

$y = \frac{5 (0)}{5 (2 \cdot (0)) - 5}$

Factor $5$ out of $- 5$ .

$y = \frac{5 (0)}{5 (2 \cdot (0)) + 5 (- 1)}$

Factor $5$ out of $5 (2 \cdot (0)) + 5 (- 1)$ .

$y = \frac{5 (0)}{5 (2 \cdot (0) - 1)}$

Cancel the common factor.

$y = \frac{5 \cdot 0}{5 (2 \cdot (0) - 1)}$

Rewrite the expression.

$y = \frac{0}{2 \cdot (0) - 1}$

Simplify the denominator.

Multiply $2$ by $0$ .

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

Subtract $1$ from $0$ .

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

Divide $0$ by $- 1$ .

$y = 0$

y-intercept(s) in point form.

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

Step 4

List the intersections.

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

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

Step 5

Find the x and y Intercepts (5x)/(2x-5)

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