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
Jim G.
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]}

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