SOLUTION: Solve and check each of the following equations for x. x over 6 - x over 8 = 1 x over x - 2 MINUS x + 1 over x EQUALS 8 over x squared - 2x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve and check each of the following equations for x. x over 6 - x over 8 = 1 x over x - 2 MINUS x + 1 over x EQUALS 8 over x squared - 2x      Log On


   

Question 116812: Solve and check each of the following equations for x.
x over 6 - x over 8 = 1

x over x - 2 MINUS x + 1 over x EQUALS 8 over x squared - 2x
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve and check each of the following equations for x.
x over 6 - x over 8 = 1
:
x%2F6 - x%2F8 = 1
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Find a value that is a multiple of 6 & 8. 24 is good one (you can use 48 also)
Multiply equation by 24
24*x%2F6 - 24*x%2F8 = 24(1)
:
Cancel out the denominators and you have:
4x - 3x = 24
:
x = 24
:
Check solution in original equation:
24%2F6 - 24%2F8 = 1
4 - 3 = 1
:
:
x over x - 2 MINUS x + 1 over x EQUALS 8 over x squared - 2x
x%2F%28%28x-2%29%29 - %28%28x%2B1%29%29%2Fx = 8%2F%28%28x%5E2+-+2x%29%29
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You can factor the last denominator to
x%2F%28%28x-2%29%29 - %28%28x%2B1%29%29%2Fx = 8%2F%28x%28x+-+2%29%29
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It's now apparent that x(x-2) is the common denominator of these fractions
Multiply equation by x(x-2)
x(x-2)*x%2F%28%28x-2%29%29 - x(x-2)*%28%28x%2B1%29%29%2Fx = x(x-2)*8%2F%28x%28x+-+2%29%29
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Cancel out the denominators and you have:
x*x - (x-2)(x+1) = 8
:
x^2 - (x^2 - x - 2) = 8; FOILed (x-2)(x+1)
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Remove the brackets, change the signs
x^2 - x^2 + x + 2 = 8
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x^2's are eliminated, subtract 2 from both sides
x = 8 - 2
:
x = 6
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Check solution in original equation:
6%2F%28%286-2%29%29 - %28%286%2B1%29%29%2F6 = 8%2F%28%286%5E2+-+2%286%29%29%29
:
6%2F4 - 7%2F6 = 8%2F24
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Convert to a common denominator
36%2F24 - 28%2F24 = 8%2F24; confirms our solution of x=6
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