Question

The restrictions on the variable in the division x+5/x+2 divided by x-3/x+1 are

Answer 1

`x \\eq-2 \text { and } x \\eq-1`

Explanation:

The restricted value is a value that makes the denominator of a function equal to zero. Thus, solving these function results in an undefined solution.

Thus,
`x \\eq-2` and
`x \\eq-1` are the restricted values for
`(x+5)/(x+2)` divided by
`(x-3)/(x+1)`

Because, substituting
`x=-2` in
`(x+5)/(x+2)`

Now, substituting
`x=-2`, we get,

`\begin{aligned}(x+5)/(x+2) &=(x+5)/(-2+2) \\&=(x+5)/(0)\end{aligned}`

Thus, results the solution undefined.

Also, substituting
`x=-1` in
`(x-3)/(x+1)`

`\begin{aligned}(x-3)/(x+1) &=(x-3)/(-1+1) \\&=(x-3)/(0)\end{aligned}`

Thus results the solution undefined.

Hence, the restricted values are
`x \\eq-2 \text { and } x \\eq-1`