91Ó°ÊÓ

When working with rational expressions, one of the most important steps is finding the common denominator.
This step is crucial because it allows us to rewrite the expressions so they can be combined easily.
In our given exercise, both terms \(\frac{3s^2}{3s-2}\) and \(\frac{13s-10}{3s-2}\) already share the common denominator \(3s - 2\).
We can directly observe this by looking at the denominators of each fraction.

When the denominators are the same, combining the fractions becomes much easier.
This is why identifying the common denominator early on can save you time and reduce potential errors.
Make sure to always check if the rational expressions have a common denominator before proceeding to the next steps.

Once we have established that the rational expressions share a common denominator, the next natural step is to combine their numerators.
This operation is quite straightforward.
Given that the denominators are already the same, we simply add the numerators together.

For our exercise, this involves taking \(3s^2\) from \(\frac{3s^2}{3s-2}\) and \(13s - 10\) from \(\frac{13s-10}{3s-2}\).
Combining them yields:
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