This week I have learned how to solve when there is two fractions by cross multiplying and how to solve by finding the common denominator by factoring.

Let’s start with an example using cross multiplying:

 

First step is to write down the restrictions. The restriction is 2.

Next is to draw the butterfly, which is basically circle the numerator of one fraction with the denominator of the other fraction. Once you got those circled, those values circled together indicate that it will be multiplied together. Write them down making sure to keep the equal sign as you are solving. Now foil in the 3 in the brackets and isolate s. You get 2. Since we wrote down that the restriction of s cannot be 2, this is extraneous.

Let’s look at another example where we have to find the common denominator instead:

In this example, it looks too complicated to do cross multiplying. The first thing we should do is write down the restrictions which is x cannot be 0 or -1. Next, we can see in the first fraction, the denominator is factorable. We can take out a 2x and get 2x(x+1). By looking at both denominators of the fractions, the common denominator would be 2x(x+1) which allows us to cancel out the denominator of the first fraction, as well as the second fraction by multiplying both fractions with the common denominator. You will then have 2x(x-2) as the nominator for the second fraction which you will distribute the 2x in the bracket. Next, move the 6 over so you can factor. Start by finding out what is common which is 2 then start factoring. The answer is -1 or 3 but since we said the restriction is 0 and -1, -1 is not a solution; therefore, the answer is 3.