The manipulation of rational expressions includes actions such as addition, subtraction, multiplication, and division, and these actions are carried out on fractions that contain polynomials in both the numerator and denominator. To execute these operations, it's necessary to identify a common denominator, factorize expressions, and eliminate common factors. These mathematical operations abide by the same core principles as those applied to numerical fractions.
| Topic | Problem | Solution |
|---|---|---|
| None | $\frac{x+\frac{1}{2}}{2+\frac{1}{x}}=$ | Given the complex fraction \(\frac{x+\frac{1}{2}}{2+\frac{1}{x}}\) |
| None | Divide. \[ \left(2 x^{5}+3 x^{3}+2 x^{2}+12 x+4\r… | Let's solve the given polynomial division problem: \(\left(2 x^{5}+3 x^{3}+2 x^{2}+12 x+4\right) \d… |