# List all x-value(s) of ordered pairs of the form (x,1) that are on the rational function f(x)=(6-2x)/((x-3)(x+5))?

Nov 9, 2017

$\left(- 7 , 1\right)$

#### Explanation:

$\text{note that "x!=3,-5" as this would make } f \left(x\right)$
$\text{undefined}$

$\text{factorising the numerator}$

$f \left(x\right) = \frac{- 2 \left(x - 3\right)}{\left(x - 3\right) \left(x + 5\right)}$

$\textcolor{w h i t e}{f \left(x\right)} = \frac{- 2 \cancel{\left(x - 3\right)}}{\cancel{\left(x - 3\right)} \left(x + 5\right)} = \frac{- 2}{x + 5}$

$\text{the cancelling of the factor "(x-3)" indicates a hole at x = 3}$

$\text{solve } \frac{- 2}{x + 5} = 1$

$\Rightarrow x + 5 = - 2$

$\Rightarrow x = - 7$

$\text{hence the only point on "f(x)" is } \left(- 7 , 1\right)$
graph{(6-2x)/((x-3)(x+5)) [-10, 10, -5, 5]}