• Multiplication: Numerators and denominators multiply. $$\frac{\Tblue{2x+1}}{\Tgreen{x-1}}\times\frac{\Tblue{x-2}}{\Tgreen{x+1}} = \frac{\Tblue{(2x+1)(x-2)}}{\Tgreen{(x-1)(x+1)}} = \frac{2x^2-3x-2}{x^2-1}$$
• Reciprocal: Numerator and denominator are swapped. $$\Big(\frac{\Tblue{x-2}}{\Tgreen{x^2+3}}\Big)^{-1} = \frac{\Tgreen{x^2+3}}{\Tblue{x-2}}$$
• Division: The numerator and denominator of the divisor are swapped and multiplied to the denominator and the numerator of the dividend. $$\frac{\Tblue{2t+1}}{\Tgreen{t-1}}\div\frac{\Tblue{t-2}}{\Tgreen{t+1}} = \frac{\Tblue{(2t+1)}\Tgreen{(t+1)}}{\Tgreen{(t-1)}\Tblue{(t-2)}} = \frac{2t^2+3t + 1}{t^2 -3t +2}$$