Month: December 2018

Adding and subtracting rational expressions with monomial numerators 

First, we should mention what a rational expression is that has a binomial denominator. A rational expression is that has a binomial denominator is an expression that has a binomial, in the place of the denominator. The binomial can be any numbers in addition or subtraction of any variable of any power.

This week in math, we learned how to multiply and divide monomials. The first step is always to factor if possible, we always need to take a look at what we’re doing; either multiplication or dividing. From previous math, we know that if it’s dividing then we need to reciprocate the fraction. The next step is to simplify all like terms, you always need to find what X can’t equal to, because the denominator cannot equal 0.

In the examples below, i forgot my non-permissible values, for the first one it’s b cannot equal 0, and same for the second one, except B and A cannot=0

Here is a video to help : https://www.youtube.com/watch?v=f1ajvLpb32E

 

Multiplying and dividing rational expressions

This week in Pre Cal, we learned how to multiply and divide rational expressions. Rational expressions are equations or quotients that have polynomials on most likely both the bottom and top, each with their own variables. It would be very difficult if not impossible to divide a polynomial by another polynomial without using a calculator. This is why we have to take steps in finding and making binomials that are easy to cancel out on both the bottom and top.

Disclaimer: When canceling out polynomials or numbers, one must be on the top of the division and the other on the bottom. It does not matter if the polynomial or number is apart of the same quotient, as long as one is somewhere on the top, and the other somewhere on the bottom. Also, if you must divide by another fraction/quotient, flip the fraction around to make it a multiplication. Ex. 1/2 ÷ 2/3 –>  1/2 x 3/2

First, we must find the “non-permissible” values, which are essential ‘x’. Contrary to the last unit, instead of ‘x’ equalling only specific numbers, in this chapter, ‘x’ cannot equal specific number. Therefore, ‘x’ would be 0 making, for example, the equation 3/0 which is impossible. Next, you must find alike polynomials, mostly binomials, by factor them. We try and make it so that a polynomial on the top and the bottom both have the same polynomial so that they can cancel each other out, making the equation easier to solve. Watch out for negatives (-) or any small details because when you cancel out polynomials, they both have to be the exact same. Then after canceling out all that is possible, you should be left with regular, real numbers. If so, you are allowed to cancel those out too. Once finished those steps, you should be left with an easy multiplication that will give you your answer.

Graphing reciprocals of linear functions

During Week 13 of Pre Cal 11, we learned about how to graph reciprocals of both linear functions and quadratic functions. Today, I will be explaining how to graph and calculate linear reciprocals. When starting, we should try and find the original linear function (y=fx). Once we find the original, we must graph it so we can keep it in relation to the reciprocal that we will soon graph. Once we find the original function (y=fx), we must turn it into a reciprocal function. See Image 1 to find out how. Then, find the x-intercepts for y=a and y=-1. These will be your invariant points, they help you graph your reciprocal function. After this, you will need to find your asymptotes, both horizontal and vertical. See Image 2 for more info. Then depending if x is negative or not, it is now time to graph the reciprocal. See image 3 for info.