I may not be writing this right...
What is the simpliest form for the product?
[(x + 1) / (x^2 – 25)] * [(x +5) / (x^2 +8x +7)]
first grouping, factor x^2-25 in the denominator. Notice now x+5 will divide out there with the x+5 in the numerator of the second.
Then, factor x^2+8x+7 in the second denominator. Notice now the x+1 factors divide out. You should be left with
1/[(x-5)(x+7)]