Question

2. How do you solve rational equations?

Answer 1

To solve rational equations, identify the equation, find the least common denominator, eliminate the denominators, simplify the equation, solve for the variable, and check the solution.

Step-by-step explanation:

To solve rational equations, follow these steps:

1. Identify the rational equation in the form of numerator/denominator = numerator/denominator.
2. Find the least common denominator (LCD) for all the denominators involved in the equation.
3. Multiply both sides of the equation by the LCD to eliminate the denominators.
4. Simplify the resulting equation, which will be in the form of a linear equation.
5. Solve the linear equation for the variable.
6. Check the solution by plugging it back into the original equation to ensure it does not result in dividing by zero.

For example, if we have the equation 1/x = 3/(x+1), we can multiply both sides by x(x+1) to eliminate the denominators, resulting in x(x+1)/x = 3(x+1)/(x+1). After simplifying, we get the linear equation x = 3(x+1). Solving this equation, we find x = 1. Finally, we can check by substituting x = 1 back into the original equation, which gives us 1/1 = 3/(1+1) or 1 = 3/2. Since this checks out, the solution is valid.

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