This week we learned how to multiply ugly fractions, which is almost exactly the same as what we were taught around middle school except with a few more extra steps. For this question factoring any numerator or denominator possible will help simplify the question. In the second line we noticed that there were matching terms on the numerator and denominator, and by following the rules of fractions anything over itself is equal to 1, because there’s no point to multiplying by 1 we’re able to just cross out the matching terms leaving us with what ever is left over as our simplified fraction.
This week we learned how to simplify “ugly” fractions. These are basically fractions that will involve factoring. A way to make these questions simpler is by crossing out common factors in the denominator and numerator of the fraction. The rule that anything divided by itself is equivalent to 1 still applies to these fraction, with that being said, by crossing out the common factors on the top and bottom of the fraction it shortens the question to it’s simplest form. We also learned that it is important to know the non-permissible values of x in the denominator. It is important to know because our denominator can never equal 0. therefore the non-permissible values of this expression are -5 and -8.
This week he learned how to graph reciprocal quadratic functions. When beginning these questions it is always easiest to start by graphing the original equation, in this example it is x squared minus 3. After graphing this draw a broken vertical line on the zeros or x-intercepts, because this graph has 2 solutions it will have 3 hyperbolas. The 2 “L” shaped hyperbolas hover right above the x-axis and almost touching the broken lines. The hyperbola on the bottom follows the same rules except it’s on the other side of the broken line.