When solving a rational equation what is the first step we must always take?
There is no such thing as a "first step" that must "always" be taken, it depends on the rational equation.
I usually try to multiply each term by the LCD, thus getting rid of the fractions
When solving a rational equation, the first step we must always take is to check for any restrictions or values that could make the rational expression undefined. This is important because certain values may cause division by zero or result in an undefined expression.
To find these restrictions, we need to identify any values that would make the denominator of the rational expression equal to zero. We set the denominator equal to zero and solve for the variable. The values of the variable that satisfy this equation are the restrictions we need to consider.
Once we have determined the restrictions, we can proceed to solve the rational equation using various methods such as simplifying, cross-multiplication, or finding a common denominator. But before we can apply these methods, it is crucial to ensure that the equation is valid for all possible values of the variable, except for the restrictions we found earlier.