Simplify each complex fraction. See Examples 5 and 6. [(y + 3)/y − 4/(y − 1)] / [(y/y + 1/y) / (y − 1) + 1/y]

Simplify each complex fraction. See Examples 5 and 6. [ (−4/3) + 12/5 ] / [ 1 − (−4/3)(12/5) ]

Simplify each complex fraction. See Examples 5 and 6. (1 + 1/x) / (1 − 1/x)

Simplify each complex fraction. See Examples 5 and 6. (x/y + y/x) / (x/y − y/x)

Simplify each complex fraction. See Examples 5 and 6. (1/(x + 1) − 1/x) / (1/x)

(Modeling) Distance from the Origin of the Nile River The Nile River in Africa is about 4000 mi long. The Nile begins as an outlet of Lake Victoria at an altitude of 7000 ft above sea level and empties into the Mediterranean Sea at sea level (0 ft). The distance from its origin in thousands of miles is related to its height above sea level in thousands of feet (x) by the following formula.

Distance = (7 − x) / (0.639x + 1.75)

For example, when the river is at an altitude of 600 ft, x = 0.6 (thousand), and the distance from the origin is

Distance ≈ (7 − 0.6) / (0.639 × 0.6 + 1.75) ≈ 3, which represents 3000 mi. (Data from The World Almanac and Book of Facts.) What is the distance from the origin of the Nile when the river has an altitude of 7000 ft?

Rationalize the denominator. 

$-\(\frac{5}{2\sqrt7}\)$

Rationalize the denominator.

$\(\frac{6+\sqrt{x}\)}{-\(\sqrt{x}\)}$

Rationalize the denominator and simplify the radical expression.

$\(\frac{\sqrt7}{5-\sqrt6}\)$