Question

What is the domain of x^2-bx +ax - ab/x2+bx-ax - ab /x2+bx+ax +ab/x2-bx-ax+ab

Answer 1

The answer is "
`\bold{(-\infty, \infty)}`"

Explanation:

Given:

`\to \bold{((x^2-bx +ax - ab)/(x2+bx-ax - ab))/((x2+bx+ax +ab)/(x2-bx-ax+ab))}`

`\to (x^2-bx +ax - ab)/(x2+bx-ax - ab) * \frac {x2-bx-ax+ab}{x2+bx+ax +ab}\\\\\to (x(x-b) +a(x - b))/(x(x+b)-a(x +b)) * \frac {x(x-b)-a(x-b)}{x(x+b)+a(x +b)}\\\\`

`\to ((x-b) (x+a))/((x+b)(x-a)) * \frac {(x-b)(x-a)}{(x+b)(x +a)}\\\\\to ((x-b))/((x+b)) * \frac {(x-b)}{(x+b)}\\\\\to ((x-b)^2)/((x+b)^2) \\\\`

`\to f(x) = ((x-b)^2)/((x+b)^2) \\\\`

So, the domain are
`\bold{(-\infty, \infty)}`