Question

What are the excluded values for `y=(x+1)/(x-3)`?

Answer 1

Excluded values: `x=3` and `y=1`

Explanation:

Given
`color(white)("XXX")y=(x+1)/(x-3)`
since division by zero is undefined, we must exclude
`color(white)("XXX")x=3`

Re-writing the given equation:
`color(white)("XXX")yx-3y=x+1`

`color(white)("XXX")yx-x=3y+1`

`color(white)("XXX")x(y-1)=3y+1`

`color(white)("XXX")x=(3y+1)/(y-1)`

and (again) since division by zero is undefined, we must exclude:
`color(white)("XXX")y=1`

This can also be seen graphically by plotting the given equation: