Question

How do you simplify and find the restrictions for `(y-3)/(y+5)`?

Answer 1

restriction: `y!=-5`

Explanation:

The given expression is already simplified and cannot be simplified any further.

To find the restriction, recall that in any fraction, the denominator must not equal to `0`. In the given fraction,

`(y-3)/(y+5)`

the denominator is expressed as a variable plus a constant. When setting the denominator to equal to `0`, you are solving for the value of `y` that will produce a denominator or `0`. The `y` value would be your restriction.

Thus,

`y+5=0`

`y+5color(white)(i)color(red)(-5)=0color(white)(i)color(red)(-5)`

`y=-5`

restriction: `color(green)(|bar(ul(color(white)(a/a)color(black)(y!=-5)color(white)(a/a)|)))`

To check your answer, you can plug in `y=-5` into the given expression to check if the denominator equals `0`. If it does, then you know the restriction is correct.

Plugging in `y=-5`,

`(y-3)/(y+5)`

`=(-5-3)/(-5+5)`

`=-8/0`

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`:.`, the restriction is correct.