Math Problem Statement

Simplify the expression \( \frac{\frac{1}{3z}}{\frac{-3}{2z} - \frac{1}{2z}} \).

Solution

Let’s simplify the given complex fraction step by step.

The given expression is:

13z32z12z\frac{\frac{1}{3z}}{\frac{-3}{2z} - \frac{1}{2z}}


Step 1: Simplify the denominator

The denominator is:

32z12z\frac{-3}{2z} - \frac{1}{2z}

Since both terms have a common denominator 2z2z, we can combine them:

312z=42z\frac{-3 - 1}{2z} = \frac{-4}{2z}

Simplify the fraction:

[ \frac{-4}{2z} = \frac{-

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Expressions
Fractions

Formulas

\( \frac{a}{b} - \frac{c}{b} = \frac{a - c}{b} \)
Simplifying complex fractions by dividing

Theorems

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Suitable Grade Level

Grades 8-10