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))?

1 Answer
Nov 9, 2017

(-7,1)

Explanation:

"note that "x!=3,-5" as this would make "f(x)
"undefined"

"factorising the numerator"

f(x)=(-2(x-3))/((x-3)(x+5))

color(white)(f(x))=(-2cancel((x-3)))/(cancel((x-3))(x+5))=(-2)/(x+5)

"the cancelling of the factor "(x-3)" indicates a hole at x = 3"

"solve "(-2)/(x+5)=1

rArrx+5=-2

rArrx=-7

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