What is the simplified form for the product Fraction 1: the quantity x plus 1 over the quantity x squared minus 25; Fraction 2: the quantity x plus 5 over the quantity x squared plus 8 times x plus 7; Find Fraction 1 times by Fraction 2.?

Question

A. The quantity x plus 1 over the quantity x plus 5 times the quantity x plus 7
B. 1 over the quantity x plus 5 times the quantity x plus 7
C. 1 over the quantity x minus 5 times the quantity x plus 7
D. 1 over the quantity x plus 5 times the quantity x minus 7

Answer 1

To simplify the product of the two fractions, we first factor the denominators:
Fraction 1: (x+1)/(x^2 - 25) = (x+1)/((x+5)(x-5))
Fraction 2: (x+5)/(x^2 + 8x + 7) = (x+5)/((x+7)(x+1))

Now we multiply the two fractions:
((x+1)*(x+5))/((x+5)*(x-5)*(x+7)*(x+1))

We can see that the factors (x+1) and (x+5) cancel out:

1/((x-5)*(x+7))

So the simplified form of the product of the two fractions is:

1/((x-5)*(x+7))

The correct answer is C. 1 over the quantity x minus 5 times the quantity x plus 7.