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- Learn About Rational Expressions with Math-a-Corn!
- By : Moyo Fagbuyi
- Ummm....what am I supposed to do?
- Do not give up my child!
- Ugh! These rational expressions are too hard! I give up!
- It is I! Math-a-Corn! I am a mythical math creature. Your tears of frustration have summoned me. What is the problem, my child?
- Huh? Who said that?
- Ah, do not worry. I can explain them to you, my child. To the chalkboard!
- I don't know how to solve these rational expressions!
- First, my child, you need to understand how to simplify rational expressions.
- x2 -4 x2 - 4x + 4
- The first step is factoring the numerator and denominator completely.
- I can do that!
- (x + 2) (x -2) (x - 2) (x - 2)
- Then you reduce the common factors in the numerator and denominator.
- (x + 2) (x -2) (x - 2) (x - 2)
- Oh, okay, I get it! Can we move onto multiplying and dividing now?
- x + 2 x - 2
- Of course, my child!
- (x + 3) (x - 4) (x + 3) (x + 8)
- x2 -x - 12 x2 + 11x + 24
- For multiplying, simplify both fractions. When it comes to reducing, my child, the factors in the numerators can be reduced with factors in either denominators. Lastly multiple the reduced fractions
- x(x +8) (x + 2) (x - 4)
- x2 + 8x x2 - 2x - 8
- (x + 3) (x - 4) (x + 3) (x + 8)
- 1 1
- Oh, that's cool!
- x x + 2
- x(x +8) (x + 2) (x - 4)
- x (x + 2)
- (2x +7) (3x -4) (2x +3) (2x -4)
- (2x - 3) (x - 5) (2x +7) (x -5)
- 2x2 -13x + 15 2x2 - 3x - 35
- 2x2 -13x + 15 2x2 - 3x - 35
- For division, change the expression to multiplication by converting the dividend to it's reciprocal. Then multiply
- (2x +7) (3x -4) (2x +3) (2x -4)
- 6x2 + 13x - 28 6x2 + x -12
- 6x2 + x -12 6x2 + 13x - 28
- Alright!
- (2x - 3) (x - 5) (2x +7) (x -5)
- 2x2 -13x + 15 2x2 - 3x - 35
- 2x -3 1
- Now, time for addition and subtraction, my child!
- 2x - 3 2x + 3
- (2x + 7) ( 3x - 4) (2x + 3) ( 3x - 4)
- 6x2 + 13x - 28 6x2 + x -12
- 1 2x + 3
- First you need to be able to find the Least common denominator, or LCD. Simplify the denominators of both fractions, my child. The LCD will contain the factors of all factors in the first denominator and the remaining unincluded factors found in the second fraction.
- 1 x2 - x - 6
- LCD : (a - 3) ( a + 2) (2a - 1)
- 1 2a2 - 7a + 3
- 1 (a - 3) ( a + 2)
- Oh, I get it! (a - 3) was already included from the first fraction, so it doesn't need to be repeated in the LCD.
- 1 (2a - 1) ( a - 3)
- 1 (a - 3) ( a + 2)
- 1 (2a - 1) ( a - 3)
- After finding the LCD, convert each fraction to an equivalent fraction with the LCD as the denominator. You can do this through multiplying the numerator and denominator by the factor the denominator needs to be equal to the LCD.
- (2a - 1) (2a - 1)
- ( a + 2) ( a + 2)
- LCD : (a - 3) ( a + 2) (2a - 1)
- (a + 2) (a - 3) ( a + 2) (2a - 1)
- (2a - 1) (a - 3) ( a + 2) (2a - 1)
- Got it!
- (2a - 1) - (a + 2) (a - 3) ( a + 2) (2a - 1)
- Since both fractions have a common denominator now, just add or subtract the numerators!
- a - 3 (a - 3) ( a + 2) (2a - 1)
- 2a - 1 - a - 2 (a - 3) ( a + 2) (2a - 1)
- If possible, I still have to simplify after adding or subtracting, right?
- 1 ( a + 2) (2a - 1)
- a - 3 (a - 3) ( a + 2) (2a - 1)
- Correct, my child!
- Magic of course!
- Ask away, my child.
- Thank you so much Math-a-Corn! I just have one more question?
- How did you write on the board, if you don't even have any fingers?
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