Simplify \( \frac{1}{1+\sqrt{5}} - \frac{1}{1-\sqrt{5}} \)

Simplify \(3\frac{1}{3} - 1\frac{1}{4} x \frac{2}{3} + 1\frac{2}{5}\)

What is the product of \( \frac{27}{5^1}(3)^{-3} \) and \( \frac{(1)^{-1}}{5} \)?

If 2257 is the result of subtracting 4577 from 7056 in base n, find n

Simplify \(2\log \frac{2}{5} - \log \frac{72}{125} + \log 9\)

Find correct to 3 decimal places \(\left(\frac{1}{0.05} + \frac{1}{5.005}\right) - (0.05 x 2.05)\)

Rationalize \( \frac{2\sqrt{3}+3\sqrt{2}}{3\sqrt{2}-2\sqrt{3}} \)

If 3 gallons of spirit containing 20% water are added to 5 gallons of another spirit containing 15% water, what percentage of the mixture is water?

Factory P produces 20,000 bags of cement per day while factory Q produces 15,000 bags per day. If P reduces production by 5% and Q increases production by 5%...