Question

How do you solve `(n+5)/(n+8)=1+6/(n+1)` and check for extraneous solutions?

Answer 1

`n = -17/3`

Explanation:

Put everything on the least common denominator of `(n + 8)(n + 1)`.

`((n + 5)(n + 1))/((n + 8)(n + 1)) = (1(n + 8)(n + 1))/((n + 8)(n + 1)) + (6(n + 8))/((n + 1)(n + 8))`

We can now solve without the denominators, considering everything is equivalent.

`n^2 + 5n + n + 5 = n^2 + 8n + n + 8 +6n + 48`

`6n - 8n - n - 6n = 56 - 5`

`-9n = 51`

`n = -17/3`

Our original restrictions on the variable are `n!= -8, -1`, and since this solution includes neither of those numbers, the solution is valid.

Hopefully this helps!