This week in Pre Calc 11 we learned how Solve Rational Equations. We learned that there are multiple ways to solve rational equations, that vary depending on what the arrangement and difficulty of the equation. The first step is to always verify that our terms are completely factored and if they are not, you must factor it and then determine the non permissible values. The first way to solve a rational equation is to move like terms to one side of the equation for example in the equation: you would first want to move the to the right side of the equation to be able to solve it in a more efficient way, because they have a common denominator you are allowed to subract 3 by 2. Another way to solve rational equations is by cross multiplying. However, this method only works if there are only two fractions, one on either side of the equal sign. For exmaple, is an example of an equation that you are able to cross multiply to help you solve it. To cross multiply, you multiply and leaving you with as your new equation. We also learned how to multiply through an equation using a common denominator. When you do this, you are putting the entire equation over a common denominator which means that it can basically cancel out when you multiply through, which will leave you with only the numerator to solve. For example, can be easily solved if you multiply each fraction by the common denominator which is This will leave you with Once we have cancelled out the numerator, you can now solve for The last method that we learned was that if the numerator’s or the denominator’s of an equation that has only two fractions (one on either side of the equal sign) are equal to one another than that means that the numerator’s or denominator’s must also be equal. This allows you to eliminate the numerator’s or the denominator’s to make it easier to solve. For example, have the same denomintor which tells you that the numerator’s will also be equal to one another, allowing you to eliminate the denominator’s, leaving you with a simplified equation of From there you must determine whether or not it’s quadraitc or linear and then you can solve for If it’s quadratic you must make the equation equal to zero and then you must factor the trinomial and find out the possible solutions for and if it’s linear you must isolate for to determine the solution. Once you have determined the solution(s), you must check to make sure that they are not any of the pre-determined non permissible values.