Rational Equations

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A rational equation is an equation that contains a fraction with at least one variable in the denominator. The goal when solving a rational equation is to isolate the variable on one side of the equation.

Here's an example:

Let's say we have the equation:

1/x + 1/3 = 1/2

To solve this equation, we can first get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which in this case is 6.

Multiplying both sides by 6, we get:

6(1/x + 1/3) = 6(1/2)

Simplifying the left side of the equation, we get:

6/x + 2 = 3

Subtracting 2 from both sides of the equation, we get:

6/x = 1

Finally, we can isolate x by cross-multiplying and solving for x:

6/x = 1

6 = x

So the solution to the equation is x = 6.

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