Simplify the rational expression. State and restrictions on the variables. X^2-5x-24/x^2-7x-40
To simplify the rational expression (x^2 - 5x - 24) / (x^2 - 7x - 40), we first factor both the numerator and denominator.
Numerator: x^2 - 5x - 24 = (x - 8)(x + 3)
Denominator: x^2 - 7x - 40 = (x - 10)(x + 4)
Now, we can rewrite the expression as:
[(x - 8)(x + 3)] / [(x - 10)(x + 4)]
This expression can't be simplified any further, so the simplified form is:
(x - 8)(x + 3) / (x - 10)(x + 4)
The restrictions on the variables are x cannot equal 10 and x cannot equal -4 because these values would make the denominator zero, which is undefined in a rational expression.