Question

How do you solve `5- \frac { a - 17} { a + 5} = \frac { a ^ { 2} - 3} { a + 5}`?

Answer 1

`a=9`

Explanation:

Given:

`5 - (a-17)/(a+5) = (a^2-3)/(a+5)`

I can see that `a=-5` will arise as a spurious solution, so let me remark from the start that it needs to be discounted as a solution, since it results in division by `0`.

Given that `a != -5`, we can multiply the equation through by `(a+5)` to get:

`a^2-3 = 5(a+5)-(a-17) = 5a+25-a+17 = 4a+42`

Subtract `4a+42` from both ends to get:

`0 = a^2-4a-45 = (a+5)(a-9)`

Since we know that `a != -5`, that leaves one solution:

`a = 9`