1. Equations & Inequalities

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

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

Solve each equation. See Example 1. x/(x-4) = 4/(x-4) + 4

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

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

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

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

Solve each equation. See Example 2. 2x/(x-2) = 5 + 4x^2/(x-2)

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

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

In Exercises 11–20, 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.

In Exercises 11–20, write an equation that expresses each relationship. Then solve the equation for y.x varies directly as z and inversely as the difference between y and w.