22. $$ \frac{2}{a b} ; \frac{a-b}{b^{2} c} $$

Question

UpStudy AI · Accepted Answer

It appears you're presenting two expressions, possibly for comparison, simplification, or to form a ratio. Let's interpret the problem as finding the ratio of the two expressions:

Given:
1. $$ \frac{2}{ab} $$
2. $$ \frac{a - b}{b^{2}c} $$

**Finding the Ratio:**

The ratio of the first expression to the second is:

$$
\frac{\frac{2}{ab}}{\frac{a - b}{b^{2}c}} = \frac{2}{ab} \times \frac{b^{2}c}{a - b}
$$

**Simplifying the Expression:**

1. Multiply the numerators and the denominators:

$$
= \frac{2 \times b^{2}c}{ab \times (a - b)}
$$

2. Simplify by canceling common terms ($$b$$):

$$
= \frac{2 \times b \times c}{a \times (a - b)}
$$

3. Final simplified form:

$$
= \frac{2bc}{a(a - b)}
$$

**Final Answer:**

$$
\frac{2}{ab} : \frac{a - b}{b^{2}c} = \frac{2bc}{\,a(a - b)\,}
$$
The ratio of $$ \frac{2}{ab} $$ to $$ \frac{a - b}{b^{2}c} $$ is $$ \frac{2bc}{a(a - b)} $$.

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