Summarize the following:
The following terms will be used throughout the examples, and are common in problems involving algebraic fractions: Numerator: The top part of a fraction (ie. (x+5)/(2x+3)). Denominator: The bottom part of the fraction (ie. (x+5)/(2x+3)). Common Denominator: This is a number that you can divide out of both the top and bottom of a fraction. For example, in the fraction 3/9, the common denominator is 3, since both numbers can be divided by 3. Factor: One number that multiples to make another. For example, the factors of 15 are 1, 3, 5, and 15. The factors of 4 are 1, 2, and 4. Simplified Equation: This involves removing all common factors and grouping similar variables together (5x + x = 6x) until you have the most basic form of a fraction, equation, or problem. If you cannot do anything more to the fraction, it is simplified. These are the exact same steps you will take to solve algebraic fractions. Take the example, 15/35. In order to simplify a fraction, we need to find a common denominator. In this case, both numbers can be divided by five, so you can remove the 5 from the fraction: 15 5 * 335 5 * 7 Now you can cross out like terms. In this case you can cross out the two fives, leaving your simplified answer, 3/7. In the previous example, you could easily remove the 5 from 15, and the same principle applies to more complex expressions like, 15x 5. Find a factor that both numbers have in common. Here, the answer is 5, since you can divide both 15x and -5 by the number five. Like before, remove the common factor and multiply it by what is "left."15x 5 = 5 * (3x 1) To check your work, simply multiply the five back into the new expression you will end up with the same numbers you started with. The same principle used in common fractions works for algebraic ones as well. This is the easiest way to simplify fractions while you work. Take the fraction: (x+2)(x-3)(x+2)(x+10) Notice how the term (x+2) is common in both the numerator (top) and denominator (bottom). As such, you can remove it to simplify the algebraic fraction, just like you removed the 5 from 15/35: (x+2)(x-3) (x-3)(x+2)(x+10) (x+10) This leaves us with our final answer: (x-3)/(x+10)
Know the vocabulary for algebraic fractions. Review how to solve simple fractions. Remove factors from algebraic expressions just like normal numbers. Know you can remove complex terms just like simple ones.