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When adding fractions, it is crucial they share a common denominator. This is the number under the fraction line that divides the numerator.
In our example, both fractions already have the same denominator, which is a huge time-saver! The denominator is \(4y + 3\).

When fractions do not have the same denominator, you must find the Least Common Denominator (LCD) before adding. The process involves:

• Identifying the denominators
• Finding the smallest number that both denominators can divide into without a remainder
• Converting each fraction to have this common denominator

Once the denominators match, you can move to the next step.

Once the denominators are the same, you only need to add the numerators. The numerator is the number above the fraction line.
Let's look at this example: \(\frac{6y + 12}{4y + 3} + \frac{2y - 6}{4y + 3}\). Here, our numerator parts are \(6y + 12\) and \(2y - 6\).

Combining the numerators step-by-step:

• Write down the expression \(6y + 12 + 2y - 6\)
• Combine like terms: \(6y + 2y\) and \(12 - 6\)
• Simplify the sums: \(8y\) and \(6\)
• Final combined numerator: \(8y + 6\)

With our numerators simplified, we are ready for the final step.

The last step in adding fractions is writing the combined fraction. This rebuilds the fraction with the new, added numerators and the common denominator from earlier.

For our example, the combined numerator is \(8y + 6\), and the common denominator remains \(4y + 3\). Putting it all together:
\[\frac{8y + 6}{4y + 3}\]
And that’s our combined fraction! This fraction presents the summed value of the two original fractions.

Remember, after obtaining the combined fraction, you should always check if it can be simplified further. Simplifying helps to express your answer in the simplest possible form.

With these steps—finding the common denominator, adding the numerators, and writing the combined fraction—you can handle any fraction addition problem with ease.