91Ó°ÊÓ

To solve rational equations, one of the first steps is isolating the rational expression. This means we want to get rid of the fraction by isolating it on one side of the equation. In our example, the equation is \( \frac{2}{3p-1} = 5 \). To isolate the fraction, we need to remove any terms not part of the rational expression.
In this specific problem, the rational expression \( \frac{2}{3p-1} \) is already isolated on one side of the equation, making it straightforward to proceed to the next step.
Understanding this concept makes handling equations involving fractions much easier.

After isolating the fraction, the next step is to eliminate the fraction. This involves clearing the denominator by multiplying both sides of the equation by the same value. This step helps us convert the fraction into a simpler form.
In our example, we have the fraction \( \frac{2}{3p-1} = 5 \). To eliminate the fraction, we multiply both sides of the equation by \( 3p - 1 \). This results in:
\( 2 = 5(3p - 1) \).
This multiplication clears out the denominator, making the equation simpler and easier to solve.

With the fraction now eliminated, the next step is to solve for the variable. This involves isolating the variable term by performing basic algebraic operations like addition, subtraction, multiplication, or division.
In our example, we start with:
\( 2 = 15p - 5 \).
First, we add 5 to both sides to get:
\( 7 = 15p \).
Then, we divide both sides by 15 to isolate the variable:
\( p = \frac{7}{15} \).
Finally, it's important to verify the solution by substituting the value back into the original equation to ensure it satisfies the equation. For our example, substituting \( p = \frac{7}{15} \) confirms the solution as the original equation holds true.
Through these steps, we can see how each concept fits together to solve the rational equation effectively.