Find the Holes in the Graph f(x)=(-x^2+5x)/(2x^2)

$f (x) = \frac{- x^{2} + 5 x}{2 x^{2}}$

Step 1

Factor $x$ out of $- x^{2} + 5 x$ .

Factor $x$ out of $- x^{2}$ .

$f (x) = \frac{x (- x) + 5 x}{2 x^{2}}$

Factor $x$ out of $5 x$ .

$f (x) = \frac{x (- x) + x \cdot 5}{2 x^{2}}$

Factor $x$ out of $x (- x) + x \cdot 5$ .

$f (x) = \frac{x (- x + 5)}{2 x^{2}}$

Step 2

Cancel the common factors.

Factor $x$ out of $2 x^{2}$ .

$f (x) = \frac{x (- x + 5)}{x (2 x)}$

Cancel the common factor.

$f (x) = \frac{x (- x + 5)}{x (2 x)}$

Rewrite the expression.

$f (x) = \frac{- x + 5}{2 x}$

Step 3

Since no factors can be removed from the denominator, there are no holes in the graph.

No holes

Step 4