What is the simplified form for the product? ((x+1)/(x^2-25))/((x+5)/(x^2+8x+7))
For unit 6 lesson 2 its C C B
since you said "product" maybe you meant
((x+1)/(x^2-25)) * ((x+5)/(x^2+8x+7))
(x+1)/((x-5)(x+5)) * (x+5)/((x+1)(x+7))
1/((x-5)(x+7))
1/(x^2+2x-35)
((x+1)/(x^2-25))/((x+5)/(x^2+8x+7))
((x+1)/(x^2-25)) * (x^2+8x+7)/(x+5)
(x^3+9x^2+15x+7)/(x^3+5x^2-25x-125)
To find the simplified form of the product, we need to simplify each term individually and then divide.
First, let's simplify the numerator:
We have (x + 1) / (x^2 - 25)
The numerator is already in its simplest form, so let's focus on the denominator. We notice that the denominator is a difference of squares, which can be factored as (x + 5)(x - 5).
So now our expression becomes: (x + 1) / ((x + 5)(x - 5))
Next, let's simplify the denominator of the second fraction:
The denominator is (x^2 + 8x + 7), which cannot be factored further.
So now we have our simplified form for the denominator: (x^2 + 8x + 7)
To simplify the whole expression, we can multiply the numerator of the first fraction by the reciprocal of the denominator of the second fraction:
((x + 1) / ((x + 5)(x - 5))) * ((x^2 + 8x + 7) / (x + 5))
Next, we can cancel out the common factor of (x + 5) in the numerator and denominator:
(x + 1) / (x - 5) * (x^2 + 8x + 7)
Finally, we can multiply the terms in the numerator and leave the denominator unchanged:
x^3 + 8x^2 + 7x + x^2 + 8x + 7
Combining like terms, we get the simplified form of the product:
x^3 + 9x^2 + 15x + 7