Explain the five-steps for solving rational equations. Can any of these steps be eliminated?
Can the order of these steps be changed? Would you add any steps to make it easier, or to make it easier to understand?
First of all it is important to understand what a "rational equation" is. It is an equation where at least one of the expressions contains a fraction (a rational expression).
As it contains a fraction it is important to be aware that some solutions may not be relevant to the answer as they could render the answer "undefined" which means there would be a zero in the denominator; for example, if (x-1) is in your denominator x cannot equal 1 `x!=1` because 1-1 = 0
- Find the lowest common denominator (LCD)
- Use LCD to eliminate any denominator
- Simplify the terms as you will now have a linear or quadratic equation and you can add or subtract like terms or move them across the equation etc.
- Solve the equation
- Check the solution for restrictions. Care to ensure that your answer does not reduce the denominator to zero.