Simplify the rational expression. State and restrictions on the variables. X^2-5x-24/x^2-7x-30
To simplify the rational expression (x^2 - 5x - 24) / (x^2 - 7x - 30), we first factor both the numerator and the denominator.
Numerator: x^2 - 5x - 24 = (x - 8)(x + 3)
Denominator: x^2 - 7x - 30 = (x - 10)(x + 3)
Now we can rewrite the expression as:
((x - 8)(x + 3)) / ((x - 10)(x + 3))
Next, we simplify by canceling out the common factor of (x + 3) in the numerator and denominator:
= (x - 8) / (x - 10)
Therefore, the simplified form of the rational expression is (x - 8) / (x - 10).
The restrictions on the variables are that x cannot equal 10 or -3, as these would make the denominator equal to zero, resulting in an undefined expression.