Final answer:
The provided expression for simplification seems to be incomplete or incorrectly typed, and thus cannot be simplified as written. Correct algebraic expressions allow the application of factoring, combining like terms, expanding, and canceling common terms to simplify them.
Step-by-step explanation:
The student has asked us to simplify the mathematical expression: (x^2+9+20)/(x^2+3-4) - (x^2+5)/(x^2+5). Unfortunately, the expression provided appears to be incorrectly typed or incomplete. Without proper polynomial structure, typical algebraic rules (like combining like terms, factoring, or expanding) cannot be applied. Simplification usually involves combining like terms, factoring, expanding expressions, or canceling out common terms in fractions.
For example, to simplify an expression you might factor polynomials to cancel out common terms. Here's a correct example for simplification: (x^2 + 5x + 4)/(x + 4) - (x^2 + 5x + 4)/(x^2 + 5x + 4), you would factor out x + 4 in the numerator of the first fraction and realize that the entire expression of the second fraction cancels out, simplifying down to just 1 - 1 = 0.
If we are to assume that simple typos occurred and instead we are looking at two correct expressions such as (x^2+5x+6)/(x+2) and (x^2+5x+4)/(x+4) as an example, we'd then factor the numerators and cancel out any common terms with the denominators, resulting in simplified expressions.