This week in math we learned about multiplying and dividing rational expressions. When working with rational expressions you must remember that the denominator cannot equal zero, so you must say what the non-permissible values, or restrictions are when answering the questions.

When multiplying rational expressions, you can either multiply right away, or you could simplify before multiplying, so that you have smaller numbers to work with. For example if you were given the expression \frac{2m^3-4m^2}{3m^2-9m} \cdot \frac{m^2-m-6}{m^2-4}, the first thing that you must do is factor where you can, after factoring the expression it would look like \frac{2m(m-2)}{3m(m-3)} \cdot \frac{(m-3)(m+2)}{(m+2)(m-2)}, once factored you would then cross out top and bottom parts of the expression that are the same, leaving you with \frac{2m^2}{3m}, you would then divide the m^2 and m to get the final simplified answer of \frac{2m}{3} with the restrictions of m≠0,3,-2,2. The picture bellow is of the expression that I just went over:

When dividing rational expressions it is the same as multiplying except you have to flip the second part of the expression to turn is into a multiplication expression. For example if you were given the expression \frac{2x+10}{8x+16} ÷ \frac{x^2-25}{(x+2)^2}, you would first factor where you can, and you would then have \frac{2(x+5)}{8(x+2)} ÷ \frac{(x+5)(x-5)}{(x+2)(x+2)}, next you would flip the second part of the expression and then you would have \frac{2(x+5)}{8(x+2)} \cdot \frac{(x+2)(x+2)}{(x-5)(x+5)}, you then cross out the top and bottom things that are the same, giving you the final answer of \frac{(x+2)}{4(x-5)} with the restrictions of x≠ -2,5,-5. The picture bellow is of the expression I just went over: