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When simplifying rational expressions, it is essential to understand how to combine fractions correctly. Here, both fractions \(-\frac{6t}{9}\) and \(-\frac{12-8t}{9}\) have the same denominator, which makes combining them a straightforward task. An important rule when handling fractions is that to combine them, their denominators must be common. With a shared denominator, the fractions can then be rewritten as one single fraction by combining their numerators.

This means we can write \(-\frac{6t}{9}\) and \(-\frac{12-8t}{9}\) as:
\[\frac{-6t - (12 - 8t)}{9}.\]

It's crucial to note how subtraction effects the sign of the terms inside the parentheses, which is something to be mindful of during simplification. This single-step process can dramatically simplify the problem, so always look for opportunities to combine fractions when solving rational expressions.

Understanding what constitutes like terms is a cornerstone of simplifying algebraic expressions. Like terms are terms that include the same variable raised to the same power. They can be combined through addition or subtraction, which is a pivotal step in simplifying expressions.

In our rational expression, after combining the fractions, we have the expression \(-6t - 12 + 8t\).
Here, \-6t\ and \8t\ are like terms because they both contain the variable \t\ raised to the first power.
Simplifying \(-6t + 8t\), we end up with \2t\.

Combining these terms gives the simplified expression:
\[2t - 12.\]

Recognizing and combining like terms is a basic skill that can significantly ease the process of simplifying algebraic and rational expressions.

Algebraic expressions are combinations of variables, numbers, and at least one arithmetic operation—such as addition or multiplication. They can represent a myriad of situations in mathematics and real life. Understanding how to simplify these expressions is essential for solving equations and working through mathematical problems efficiently.

In this particular example, we start with a rational expression: \(-\frac{6t}{9} - \frac{12-8t}{9}\).
The goal is to make it as simple as possible using algebraic principles.
Combining the fractions and like terms, we arrive at:
\[\frac{2t - 12}{9}.\]

This expression shows the power of algebra in reducing complex problems into simpler forms that are easier to interpret and solve. Familiarizing with tactics such as finding common denominators and collecting like terms will enable you to tackle a wide range of algebraic problems successfully.