x^2+2x-15/4x^2/x^2-25/2x-10

You need to use parentheses to clarify the meaning of what you wrote. You can't have a four-story fraction with three / signs

x^2+2x-15 factors into (x+5)(x-3)
There is also an (x+5) factor in x^2-25,and an (x-5) factor in 2x-10.

That should lead to some cancellations

To simplify the expression, let's break it down step by step:

1. First, factor the numerator and denominator:
- The numerator, x^2 + 2x - 15, factors into (x + 5)(x - 3).
- The denominator, 4x^2/x^2 - 25/2x - 10, can be broken down further:
- The first term, 4x^2, doesn't have any common factors to cancel.
- In the second term, x^2 - 25, recognize that it is a difference of squares, so it factors into (x + 5)(x - 5).
- Finally, the last term, 2x - 10, has a common factor of 2, so it factors into 2(x - 5).

Therefore, the denominator factors into 4x^2/((x + 5)(x - 5)(x - 5)(x - 3)).

2. Now, simplify the expression by canceling out common factors:
- The numerator, (x + 5)(x - 3), and the denominator, (x + 5)(x - 5)(x - 5)(x - 3), have common factors of (x + 5) and (x - 3). These factors cancel each other out, leaving:
- The simplified expression becomes (x + 5)(x - 3) / (4x^2)(x - 5)(x - 5).

Therefore, the simplified form of the expression x^2 + 2x - 15 / 4x^2 / x^2 - 25 / 2x - 10 is (x + 5)(x - 3) / (4x^2)(x - 5)(x - 5).