Blog #4 partial fractions

Welcome to another day of Mathland!! Today In the Mathland I was practicing problems on a difficult process known as partial fractions. It's basically finding two smaller fractions that make up a bigger rational fraction. But through this blog post, I hope I can make your life easier with these tough thingies. 

To solve any partial fractions we must:

1. Multiply by the LCD

2. Distribute

3. Bring terms again

4. Factor the variables out

5. Equate with other side

6. Solve a system of equations.

7. Write as a partial fraction.

As seen in number nine I factored the denominator into two terms and used terms A and B in order to represent the coefficients. Then I found a common denominator which was x^2 + x and distributed the terms. I rearranged the terms together and factored the variables in order to help me equate. This equation was 0x+1 = x(A+B) + A. In this way (a+b) would have to equal 0 and A =1 . If we were to solve the system of equations we would find that b=-1 . Using substitution I would right this as a partial fraction. 

Of course this is just a basic lesson on how to do these things but these are the mains steps for more difficult problems.