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The first thing to do when simplifying an algebraic fraction is to simplify each part of the fraction. Start with the top part, factoring out as many numbers as you can.  For an example, this section will use the problem: 9x-315x+6 Start with the numerator: 9x – 3. There is a common factor to both 9x and -3: 3. Factor out the 3 like you would any other number, leaving you with 3 * (3x-1). This is your new numerator: 3(3x-1)15x+6 Continuing the example from above, isolate the denominator, 15x+6. Again, look for a number that can divide into both parts. Here you can again factor out a 3, leaving you with 3 * (5x +2). Write in your new denominator: 3(3x-1)3(5x+2) This is the stage where you really get to simplify the fraction. Take any terms that are in both the numerator and the denominator and remove them. In this case, we can remove the 3 from both the top and the bottom.  3(3x-1)    →     (3x-1)3(5x+2)   →       (5x+2) A fraction is simplified when there are no more common factors in the top or the bottom. Remember that you cannot remove factors from inside the parenthesis – in the example problem you cannot factor out the x from 3x and 5x, since the full terms are actually (3x -1) and (5x + 2). Thus, the example is fully simplified, making the final answer: (3x-1)(5x+2) The best way to learn is to keep trying to simplify algebraic fractions. The answers are underneath the problems. 4(x+2)(x-13)(4x+8) Answer: (x=13) 2x2-x5x Answer:(2x-1)/5
Find a common factor in the numerator, or top part of the fraction. Find a common factor in the denominator. Remove like terms. Know when the equation is fully simplified. Try a practice problem.