Question

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Answer 1

\[\frac{(x+5)(x-1)}{(x-5)(x+1)}\]

Answer 2

https://mathway.com/graph

Answer 3

x=-5
x=1
How get that aster?

Answer 4

Put numerator=0

Answer 5

yes the answer x=-5
x=1
If I set denominator zero than x=5 ; x=-1

Answer 6

Never put denominator=0 ..Those are places where the function isnt defined. For getting solution ALWAYS put numerator=0

Answer 7

my answer not match with the graph

Answer 8

ok thank

Answer 9

yw :)

Answer 10

put zero on the top not bottom?

Answer 11

The reason you "set" the numerator to zero is because when you have a function f(x), to find the roots (or x-intercepts) of the function, you find where f(x) = 0.

Therefore if \[f(x) = \frac{ (x+5)(x-1) }{ (x-5)(x+1) } = 0\]
then
\[\frac{ (x+5)(x-1) }{ (x-5)(x+1) } * (x-5)(x+1) = 0 * (x-5)(x+1)\]
and
(x+5)(x-1) = 0

Answer 12

However to graph your function, you would also need to find the vertical asymtotes, where f(x) does not exist.
If
\[f(x) = \frac{ g(x) }{ h(x) }\]
The function f(x) is undefined when h(x) = 0
In this case h(x) = (x-5)(x+1) so the function is not defined when 0 = (x-5)(x+1) and the vertical asymtotes are located at x = 5 and x=-1.