1. Equations & Inequalities

Solve each equation. See Example 1. (2x+5)/2 - 3x/(x-2) = x

Solve each equation. (4x+3)/4 - 2x/(x+1) = x

Solve each equation. x/(x-3) = 3/(x-3) + 3

Solve each equation. x/(x-4) = 4/(x-4) + 4

Solve each equation. 3/(x²+x-2) - 1/(x²-1) = 7/(2x²+6x+4)

Solve each equation. See Example 2. (4x+3)/(x+1) + 2/x = 1/(x²+x)

Solve each equation. x/(x-1) - 1/(x+1) = 2/(x²-1)

Solve each equation. (x+4)/2x = (x-1)/3

Solve each equation. 2x/(x-2) = 5 + 4x²/(x-2)

Solve each equation. 3x²/(x-2) + 2 = x/(x-1)

Solve each equation for the specified variable. (Assume all denominators are nonzero.) 1/R=1/r_1 + 1/r_2, for R

Solve each equation. 10/(4x-4) = 1 /(1-x)

In Exercises 45–46, describe in words the variation shown by the given equation. z = kx^2 √y

Describe in words the variation shown by the given equation. $z = \frac{k\sqrt{x}}{y^2}$

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as z and inversely as the sum of y and w.