The First step in the process is to find the least common denominator of all the fractions in the equation. The second step is to multiply the terms with the least common denominator to eliminate the fractions. The third step is to simplify the terms. The Fourth step is to solve the equation. The fifth step is to check the solution to make sure that the solution does not make the fraction undefined. The steps cannot be reordered or eliminated. They are all necessary steps to completing the process. If steps were replaced in this sequence the data wouldn’t be consistent with the correct answer.
A rational expression does not start with an "equals" sign. It is not a full equation. A rational equation does start out as an equation, complete with "equals" sign.
If you are faced with a single rational expression (polynomial in the numerator and polynomial in the denominator) and you want to simplify it, factor everything and cancel factors that are in both the numerator and denominator. (Once you start looking at graphs of rational functions, those "canceled" factors are what lead to holes in the graph.)
For instance: Say you started with (x+2)/(x2+5x+6). Factor the denominator. Now the rational expression looks like (x+2)/[(x+2)(x+3)]. The (x+2) factor "cancels" and you are left with 1/(x+3) which is in simplest terms.
If you are faced with the sum or difference of two rational expressions, find the least common denominator. Multiply each term by "1" to make the denominators the same, combine like terms in the numerator, and simplify.
For instance: Say you started with 1/(x2+5x+6) -1/(x2+7x+10). In order to find the least common denominator, factor both denominators. Now you have 1/[(x+2)(x+3)] -1/[(x+5)(x+2)], and the least common denominator is (x+2)(x+3)(x+5) (Do you see why?). The first term is missing the (x+5) factor in the denominator, so multiply it by (x+5)/(x+5) (That's what I mean by multiply by "1"). Multiply the second term by...