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Math made easy <3

Math made easy <3. Lauren Pak Per. 1 9/27/11. Partial Fractions. For Partial Fractions it is important to be able to split the equation into the appropriate parts. 1. Make Substitute nominator with A, B, or C variables

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Math made easy <3

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  1. Math made easy <3 Lauren Pak Per. 1 9/27/11 Lauren Pak, Period 1

  2. Partial Fractions • For Partial Fractions it is important to be able to split the equation into the appropriate parts. • 1. Make Substitute nominator with A, B, or C variables • 2. Find a common Denominator and simplify the equation. Make each denominator (quantity) the bottom of the A, B, C variables • Make the new partial fraction equal to the original numerator. • 4. Solve for A, B, and C by making x= integers. • Plug in the solved numbers into the variables. • Solve! The integral easily!  Lauren Pak, Period 1

  3. For partial fractions… • When making the equations for the partial fractions, the substitutions at the top can be one of the following depending on the numerator of the fraction. • There are three diff ways to work the A, B, and Cs!  Lauren Pak, Period 1

  4. Lets try it  • 5x= A and 3=B • Common denominator is (x+1)(x-3) • Multiply the top and bottom to simplify • 5x-3 is the original numerator which the equation will equal to. • Now by plugging in integers, solve for the variables. • For example, by trying to make one variable equal 0, it helps us solve for the still there variable! • In the end, plug it all in to replace the substituting A and B equations! Lauren Pak, Period 1

  5. Some quirky rules… • When the denominator of the fraction is a square of a quantity, the bottom of the Partial Fraction will be different from what you would expect normally. • Same is with a cubed quantity.  Like this Lauren Pak, Period 1

  6. When you are stuck! • When you first look at the integral, see if you can simplify the equation at all so that you can factor and thus easily use partial fractions! Ta da! • Use long division, where you try to get the same power in order to cancel and solve! • Ex. Times x^2 by 2x in order to get 2x^3! Lauren Pak, Period 1

  7. And sometimes! • You can’t solve for all of the A, B, C’s easily! • When that happens, plug in the solved variables like in this case A, in order to find the others! Lauren Pak, Period 1

  8. And thaaats it! Yay for partial fractions being so fuN! Lauren Pak, Period 1

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