Final answer:
To simplify and solve quadratic equations like (x² + 0.0211x - 0.0211 = 0), the quadratic formula is used, with considerations for both possible signs in the numerator.
Step-by-step explanation:
The original expression provided by the student is (x+3)/(x²-2x-3). To simplify and solve expressions or equations like the ones presented (for example, x² + 0.0211x - 0.0211 = 0 or similar quadratic forms), we can use the quadratic formula, which applies to equations of the form ax² + bx + c = 0.
The key process in simplifying or solving includes factoring, using the quadratic formula, and understanding the properties of exponents including negative exponents, which imply that an element is in the denominator (for instance, x⁻¹ = 1/x).
When solving quadratic equations like x² + 0.0211x - 0.0211 = 0, we evaluate using both potential signs for the square root in the quadratic formula resulting in values such as x = 0.0216 or x = -0.0224.
For higher degree polynomials that cannot be solved using the quadratic formula, numerical methods or graphing calculators might be necessary, for instance x = 0.027 atm obtained through such means.
Dividing and multiplying using exponents follows specific rules as well; to divide, you subtract exponents, and to multiply, you add them.
Negative exponents also play a crucial role in these operations, reversing the base to the denominator position.