Question

How do you simplify and find the restrictions for `(x^2+x)/(x^2+2x)`?

Answer 1

`(x+1)/(x+2); x!=-2, 0`

Explanation:

`(x^2+x)/(x^2+2x)`

`=(cancelx(x+1))/(cancelx(x+2))` `->` factor and cancel

`=(x+1)/(x+2)`

The restrictions consist of `x`-values that make the denominator zero.

Set the original expression's denominator equal to `0`:

`x^2+2x != 0`
`x(x+2)!= 0`
`x!= 0` and `x+2!= 0 => x!=-2`

Set the simplified expression's denominator equal to `0`:
`x+2!=0`
`x!=-2`
This is the same answer as above, but sometimes there are additional restricted values that result from the simplified expression.

`(x+1)/(x+2); x!=-2, 0`

Answer 2

`(x+1)/(x+2)` [`x!=0` and `x!=-2`]

Explanation:

Expression `=(x^2+x)/(x^2+2x)`

`= (x(x+1))/(x(x+2))`

If `x!=0`

Expression `=(x+1)/(x+2)`

Hence, Expression is defined `forall x in RR != -2`

`:.`Expression `=(x+1)/(x+2)` [`x!=0` and `x!=-2`]