SOLUTION: Determine the total area of the trapezoid shown below. Express your answer as a rational expression (single fraction) in factored form. Using the formula 1/2(x1 + X2) X h Whe

Algebra ->  Expressions-with-variables -> SOLUTION: Determine the total area of the trapezoid shown below. Express your answer as a rational expression (single fraction) in factored form. Using the formula 1/2(x1 + X2) X h Whe      Log On


   

Question 165066: Determine the total area of the trapezoid shown below. Express your answer as a rational expression (single fraction) in factored form.
Using the formula 1/2(x1 + X2) X h
When:
x1 = (x-2) / (1 + x)
x2 = (12x - 3) / (2x^2 - x - 3)
h = 27 - 8x^3
Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
the answer I get is:

Email me and I will send you a .pdf file with the work.
.
justin.sheppard.tech@hotmail.com
As a tutor, I only see the question. I do not see who posted the question. It is easiest for me to work the problem out on a piece of paper, scan the paper, and email it to the student. There is a lot less typing and looking at a computer screen.
Here is my work:
Given
%281%2F2%29%28x1%2Bx2%29h area of a trapezoid
where
x1=%28x-2%29%2F%281%2Bx%29
x2=%2812x-3%29%2F%282x%5E2-x-3%29
h=27-8%5E3
%281%2F2%29%28%28x-2%29%2F%281%2Bx%29%2B%2812x-3%29%2F%282x%5E2-x-3%29%29%2827-8x%5E3%29
Factor everything to it's simplest form and you get

Note: Use the rule for factoring the difference of two perfect cubes when factoring (27-8x^3) which is A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%29
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In order to add two expressions you need to have the same denominator (you must have the same thing on the bottom of the fraction)
You must find the LCM which in this case is %281%2Bx%29%28x-3%29%28x%2B2%29
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any number divided by the same number equals 1
any number times 1=itself
therefore you can multiply the numerator and denominator in this problem by whatever is missing to make the denominator = to the LCM.
In this case the LEFT expression is missing %28x-3%29%28x%2B2%29 so you would multiply the expression by %28%28x-3%29%28x%2B2%29%2F%28x-3%29%28x%2B2%29%29
.
In this case the RIGHT expression is missing %281%2Bx%29 so you would multiply the expression by %28%28x%2B1%29%2F%28x%2B1%29%29
.
so we get
.
%28%283-2x%29%289%2B3x%2B3x%5E2%29%29
.Multiply through and you get

.
In true factored form I guess it would be written:

Tutoring available
Contact justin.sheppard.tech@hotmail.com for details