The problem asks us to solve for $x$ in two equations: a) $\frac{a}{x} = \frac{b}{c}$ b) $\frac{ab}{x} = r + 1$

1. Problem Description

The problem asks us to solve for $x$ in two equations:

a) $\frac{a}{x} = \frac{b}{c}$

b) $\frac{ab}{x} = r + 1$

2. Solution Steps

a) To solve $\frac{a}{x} = \frac{b}{c}$ for $x$, we can cross-multiply:

$a \cdot c = b \cdot x$

$ac = bx$

Then, divide both sides by $b$:

$x = \frac{ac}{b}$

b) To solve $\frac{ab}{x} = r + 1$ for $x$, we can multiply both sides by $x$:

$ab = x(r + 1)$

Then, divide both sides by $(r + 1)$:

$x = \frac{ab}{r + 1}$

3. Final Answer

a) $x = \frac{ac}{b}$

b) $x = \frac{ab}{r + 1}$