Find the Holes in the Graph f(x)=(x^2-3x-10)/(4x-10)

$f (x) = \frac{x^{2} - 3 x - 10}{4 x - 10}$

Factor $x^{2} - 3 x - 10$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Write the factored form using these integers.

$f (x) = \frac{(x - 5) (x + 2)}{4 x - 10}$

Factor $2$ out of $4 x - 10$ .

Factor $2$ out of $4 x$ .

$f (x) = \frac{(x - 5) (x + 2)}{2 (2 x) - 10}$

Factor $2$ out of $- 10$ .

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

Factor $2$ out of $2 (2 x) + 2 (- 5)$ .

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

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

No holes

Find the Holes in the Graph f(x)=(x^2-3x-10)/(4x-10)

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