x^2-25 over x^2+7x, divided by x^2+7x+10 over x^2+9x+14.
I found the solution to be x-5 over x, is this correct?
yes,
don't forget the restrictions that
x cannot be equal to -2,-5,-7
(or else you divided by zero)
To divide these fractions, you can simplify by multiplying the first fraction by the reciprocal of the second fraction.
First, let's simplify the fractions separately:
The first fraction can be factored as (x^2 - 25) / (x^2 + 7x) = (x - 5)(x + 5) / (x(x + 7)).
The second fraction can be factored as (x^2 + 7x + 10) / (x^2 + 9x + 14) = (x + 2)(x + 5) / (x + 2)(x + 7).
Now, simplify the expression by canceling out the common factors:
[(x - 5)(x + 5) / (x(x + 7))] / [(x + 2)(x + 5) / (x + 2)(x + 7)].
Canceling out the common factors, you are left with (x - 5) / x.
Therefore, the simplified expression is (x - 5) / x.
So, your solution of (x - 5) / x is correct!