(x^2+4x-21/x^2-6x-16)*(x^2-8x+15/x^2+9x+14)
To simplify the expression:
`(x^2+4x-21)/(x^2-6x-16) * (x^2-8x+15)/(x^2+9x+14)`
We can simplify each fraction separately and then multiply the results.
Let's start with the first fraction `(x^2+4x-21)/(x^2-6x-16)`:
1. Factorize the numerator and denominator:
`(x^2+4x-21)` can be factored as `(x+7)(x-3)`
`(x^2-6x-16)` can be factored as `(x+2)(x-8)`
So the first fraction becomes: `(x+7)(x-3)/(x+2)(x-8)`
Now let's move on to the second fraction `(x^2-8x+15)/(x^2+9x+14)`:
1. Factorize the numerator and denominator:
`(x^2-8x+15)` can be factored as `(x-3)(x-5)`
`(x^2+9x+14)` cannot be factored any further.
So the second fraction remains as `(x-3)(x-5)/(x^2+9x+14)`
Now that we have both fractions simplified, we can multiply them:
`(x+7)(x-3)/(x+2)(x-8) * (x-3)(x-5)/(x^2+9x+14)`
To multiply these fractions, multiply the numerators together and the denominators together:
Numerator: (x + 7)(x - 3)(x - 3)(x - 5)
Denominator: (x + 2)(x - 8)(x^2 + 9x + 14)
The resulting expression is:
`(x + 7)(x - 3)(x - 5)(x - 3)/(x + 2)(x - 8)(x^2 + 9x + 14)`
This is the simplified form of the given expression.