To simplify the expression, we factor each polynomial:
(x^2 - 2x - 24) / (x^2 + 7x + 12) * (x^2 - 1) / (x - 6)
Factoring the polynomials, we get:
(x - 6)(x + 4) / (x + 3)(x + 4) * (x + 1)(x - 1) / (x - 6)
Now, we can cancel out the common factors:
((x - 6) * x * (x + 1) * (x - 1)) / ((x + 3) * (x - 6))
The final simplified expression is:
x(x^2 - 1) / (x + 3)
Therefore, the simplified rational expression is x(x^2 - 1) / (x + 3). The restriction on the variable is x ≠ -3 and x ≠ 6.
Simplify each rational expression. State any restrictions on the variable.
X^2-2x-24/x^2+7x+12 * x^2-1/x-6
5 answers
wrong. It is (x^2 - 1) / (x + 3)
Apologies for the oversight. Let's simplify the expression again:
(x^2 - 2x - 24) / (x^2 + 7x + 12) * (x^2 - 1) / (x - 6)
Factoring the polynomials in the numerator, we have:
(x - 6)(x + 4) / (x + 3)(x + 4) * (x + 1)(x - 1) / (x - 6)
Now, simplifying and canceling out common factors:
(x - 6)(x + 1)(x - 1) / (x + 3)
Simplifying further:
(x^2 - 1) / (x + 3)
So, the correct simplified expression is (x^2 - 1) / (x + 3). The restriction on the variable is x ≠ -3.
(x^2 - 2x - 24) / (x^2 + 7x + 12) * (x^2 - 1) / (x - 6)
Factoring the polynomials in the numerator, we have:
(x - 6)(x + 4) / (x + 3)(x + 4) * (x + 1)(x - 1) / (x - 6)
Now, simplifying and canceling out common factors:
(x - 6)(x + 1)(x - 1) / (x + 3)
Simplifying further:
(x^2 - 1) / (x + 3)
So, the correct simplified expression is (x^2 - 1) / (x + 3). The restriction on the variable is x ≠ -3.
also, from the original equation, x ≠ -3, -4, 6
Yes, you are correct. Thank you for pointing that out.
The correct simplified expression is (x^2 - 1) / (x + 3) and the restrictions on the variable are x ≠ -3, -4, 6. Thank you for your patience.
The correct simplified expression is (x^2 - 1) / (x + 3) and the restrictions on the variable are x ≠ -3, -4, 6. Thank you for your patience.