Please help with solving fractional equations!

G

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My daughter is stuck on this type of fractional equation in her Jacobs Algebra 1 text. I believe they want her to solve for x using the quadratic formula. We have the answer key but if you could explain the step-by-step followed to get to the answers, we would greatly appreciate it! Thanks so much.

1/(x+2) - 1/x = 10



and another:

1/x - 1/(x-1) = 5
 
cchisholm said:
solve for x using the quadratic formula
1/(x+2) - 1/x = 10
Click to expand...

Domain Considerations:

x != -2
x != 0

You must understand where these exclusions arise. A denominator turns zero! Can't have that.

After makign sure the denominators are NOT zero, simply multiply by the least common denominator. You can spend some time finding the "least" or you can just proceed a piece at a time.

1/(x+2) - 1/x = 10

Multiply by 'x' (Note: You can do this if you know it isn't zero.)

x*[1/(x+2) - 1/x] = x*10
x/(x+2) - x/x = 10*x
x/(x+2) - 1 = 10*x

Multiply by 'x+2'

(x+2)*[x/(x+2) - 1] = (x+2)*10*x
x*(x+2)/(x+2) - (x+2) = 10*x*(x+2)
x - (x+2) = 10*x*(x+2)
x - x - 2 = 10*x*(x+2)
-2 = 10*x*(x+2) (Note: The whole point, up to now, was just to get rid of the fractions. If you still have some denominators, other than '1', something went wrong.

Divide by 2

-1 = 5*x*(x+2)
-1 = 5*x^2 + 10*x
5*x^2 + 10*x +1 = 0

THAT is ready for the Quadratic formula. If you get x = -2 or x = 0, just throw them out.


1/x - 1/(x-1) = 5
Click to expand...
Same thing.

Domain Considerations
Multiply by 'x'
Multiply by 'x-1'
Simplify and Rearrange
Use the Quadratic Formula
Discard Fake Answers (q.v. Domain Considerations)
Check your results in the Original Equation
 
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Cool. Thanks.

Is there a list of these codes?
 
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