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When you come across rational equations, dealing with fractions can be tricky. A robust technique to handle these is 'clearing denominators'. This involves getting rid of the fractions by multiplying both sides of the equation by a common denominator. This common denominator should be the product of all the unique denominators in your equation.

In our exercise, to clear the denominators, we multiply each term by the product of the denominators, which are 'x' and 'x+5'. Doing so, it's crucial to apply the multiplication across the entire equation to maintain equality. As a result, the equation simplifies to remove fractions entirely, making it easier to solve. This step sets a clear path forward to solve an equation that once had intimidating fractions.

Once fractions are out of the way, the next step is simplifying the equation. Simplification makes equations more manageable and prepares them for solving. This can involve expanding products, combining like terms, and reducing expressions to their simplest form.

In our exercise, we began by expanding the product on the right-hand side of the equation. Expansion involves using distributive property to multiply and combine like terms, which often leads to a polynomial equation. It's important to take care while simplifying to ensure that each term is combined correctly and no errors are introduced, as this can lead to incorrect solutions.

Rearranging an equation is an essential skill in algebra. After simplifying the equation, you may need to move terms around to isolate the variable you're solving for - in this case, 'x'. This can involve adding or subtracting terms from both sides to get 'x' by itself, or sometimes dividing or multiplying if required.

During the rearrangement in our exercise, we subtracted like terms from both sides to get zero on one side, leaving us with an equation that could be easily solved for 'x'. It's vital to consistently perform the same operation on both sides to maintain the balance of the equation. The final rearrangement provides a clear solution for 'x', which is the goal of solving the equation.