Simplify:
(X^2+X-2)/(X^2-9)/(X^2-6X-16)/(X^2-6X+9)
I have the answer as (X-3)(X-1)/(X-8)(X+3) is this right?
[(X-3)(X-1)] / [(X-8)(X+3)]
is right
Thanks so much
To simplify the given expression, we'll need to factorize each of the quadratics in the denominators and look for common factors to cancel out.
The expression is: (X^2+X-2)/(X^2-9)/(X^2-6X-16)/(X^2-6X+9)
1. Factorize the first denominator: X^2-9 = (X+3)(X-3)
2. Factorize the second denominator: X^2-6X-16 = (X-8)(X+2)
3. Factorize the third denominator: X^2-6X+9 = (X-3)(X-3)
Now we can rewrite the expression using the factored denominators:
(X^2+X-2) / [(X+3)(X-3)] / [(X-8)(X+2)] / [(X-3)(X-3)]
Next, we can look for common factors to simplify further:
1. The (X-3) factor appears in both the second and fourth denominators. We can cancel it out.
After canceling the common factors, we get:
(X^2+X-2) / [(X+3)] / [(X-8)(X+2)] / (X-3)
Now, we can express the simplified form as a single fraction:
(X^2+X-2) / [(X+3)(X-8)(X+2)(X-3)]
So, the simplified expression is (X^2+X-2) / [(X+3)(X-8)(X+2)(X-3)].
Therefore, the answer you provided, (X-3)(X-1)/(X-8)(X+3), is not correct.