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$-\frac{2b}{3}-\frac{3\left(a-2b\right)}{5}$

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Function transformation rules

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Q.

-\frac{2b}{3}-\frac{3\left(a-2b\right)}{5}

Identify Terms: Identify the terms in the expression that need to be simplified. $\newline$ The expression has two terms: $-\frac{2b}{3}$ and $-\frac{3(a-2b)}{5}.$
Distribute $-3$ : Simplify the second term by distributing the $-3$ across the parentheses. $\newline$ $-\frac{3(a-2b)}{5} = -\frac{3a}{5} + \frac{6b}{5}$
Combine Like Terms: Combine the like terms from the first term and the simplified second term. $\newline$ $-\frac{2b}{3} + \frac{6b}{5} - \frac{3a}{5}$
Find Common Denominator: Find a common denominator for the terms involving $b$ . The common denominator for $3$ and $5$ is $15$ . $-\frac{2b}{3}$ becomes $-\frac{10b}{15}$ and $\frac{6b}{5}$ becomes $\frac{18b}{15}$ .
Combine Terms: Combine the terms with the common denominator. $\newline$ $-\frac{10b}{15} + \frac{18b}{15} = \frac{8b}{15}$
Write Final Expression: Write the final simplified expression by combining the result from Step $5$ with the term involving $a$ from Step $3$ . $\frac{8b}{15} - \frac{3a}{5}$

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