Lesson: Rational Equations
Alright, it is finally my turn to create a scribe post. I will try to make this post the best ever and easy for all of you guys to understand. I will create a new standard for scribe post. Okay let's start.Key Terms
Factor - One of two or more expressions that are multiplied to get a product.
Example: 4 X 5 = 20
The 4 and 5 are the factors. 1, 2, 4, 5, 10, 20 are all factors of 20.
Expression - a combination of numbers, operators, and grouping symbols (such as brackets) arranged in a meaningful way which can be evaluated.
Example: (X - 1)
(X - 1) is the expression.
Free Variable - a variable which the value held in that variable is changeable.
Example: X
X can have a value of anything. The value of X is changeable at any point.
Bound Variable - a variable that stays constant at all times.
Example: ∏ (Pi)
The value of Pi never changes. It will always be 3.14...
LCD - this stands for the least common denominator. The least common denominator is the least common multiple of the denominators of a set of fractions.
Example: (2 / 5) + (6 / 5) = (8/5) or {(X + 4) / (X - 7)} + (2/6)
In the first equation, the LCD is 5. The second equation the LCD is 6(X - 7)
Restricted Values: values that the final answer cannot be.
Quadratic Formula:
A represents the first term. B represents the middle term. C represents the last term.
The Lesson
I think the simplest way for someone to learn this material is by getting you a step-by-step guide of the process.
The equation will be {6x / (x - 5)} = 2 + {6 / (2x - 2)}
Step 1: Factoring (if possible)
Factoring is taking each expression to it's simplest form.
This equation will be factored to be {6x / (x - 5)} = 2 + {3 / (x - 1)}
Step 2: Find the LCD
Now that the denominators are in their simplest form, we must multiple each denominator.
(X - 5)(X - 1) = X² - 6X + 5
Step 3: Determining the restricted values
To find the restricted values, we take the simplified expressions above and solve for X.
X - 5 = 0 | X - 1 = 0
x = 5 X = 1
Therefore, the restricted values for this equation are 1 and 5.
Step 4: Multiply each term by the LCD
We must now get rid of the denominators. Multiply each numerator by the LCD.
Now the equation becomes: 6x² - 6 = 2x² - 12x + 12 + 3x -15
Match like terms: 6x² - 2x² + 12x - 3x - 6 - 12 + 15 = 0
Combine like terms: 4x² + 9x - 3 = 0
Step 5: Solve Algebraically
The final step is just to solve for X.
Normally we would factor the equation and find x. In this case, the equation isn't factor-able. This means we will have to solve by using the quadratic formula.
X = - (9) +/- √(9)² + 4 (4) (-3)
2 (-3)
X = - 9 +/- √33
-6
X = - 9 + √33 and X = - 9 - √33
-6 -6
Summary
In this post, I give you the definition of some terms. Then, I showed you how rational equations are solves. Basically, if you follow the steps I can guarantee 90% of the time you will not get the wrong answer.
Bibliography
http://en.wikipedia.org/wiki/Expression_(mathematics)
http://www.math.com/school/subject1/lessons/S1U3L1GL.html
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Next Scrible...le_joséph. I'm sure he is eager to make his scribe post. Enjoy! :)
posted by NT* @ 5:07 PM
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