SOLUTION: solve each of the equation. indicate the LCD -1/x-5=x-6/x-5

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Question 165640: solve each of the equation. indicate the LCD
-1/x-5=x-6/x-5
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve each of the equation. indicate the LCD
-1/(x-5) = (x-6)/(x-5)
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LCD = x-5
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Since both fractions have the same denominator, combine the numerators to get:
[-1+x-6]/(x-5)
= (x-7)/(x-5)
====================
Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-1%2F%28x-5%29=%28x-6%29%2F%28x-5%29 Start with the given equation


-1%28x-5%29=%28x-6%29%28x-5%29 Cross multiply


-1%28x-5%29=x%5E2-11x%2B30 FOIL


-x%2B5=x%5E2-11x%2B30 Distribute


0=x%5E2-11x%2B30%2Bx-5 Add x to both sides. Subtract 5 from both sides.


0=x%5E2-10x%2B25 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-10, and c=25


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%281%29%2825%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-10, and c=25


x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%281%29%2825%29+%29%29%2F%282%281%29%29 Negate -10 to get 10.


x+=+%2810+%2B-+sqrt%28+100-4%281%29%2825%29+%29%29%2F%282%281%29%29 Square -10 to get 100.


x+=+%2810+%2B-+sqrt%28+100-100+%29%29%2F%282%281%29%29 Multiply 4%281%29%2825%29 to get 100


x+=+%2810+%2B-+sqrt%28+0+%29%29%2F%282%281%29%29 Subtract 100 from 100 to get 0


x+=+%2810+%2B-+sqrt%28+0+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2810+%2B-+0%29%2F%282%29 Take the square root of 0 to get 0.


x+=+%2810+%2B+0%29%2F%282%29 or x+=+%2810+-+0%29%2F%282%29 Break up the expression.


x+=+%2810%29%2F%282%29 or x+=++%2810%29%2F%282%29 Combine like terms.


x+=+5 or x+=+5 Simplify.


So the possible solution is x+=+5


However, we must check the answer.


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Check:


-1%2F%28x-5%29=%28x-6%29%2F%28x-5%29 Start with the given equation


-1%2F%285-5%29=%285-6%29%2F%285-5%29 Plug in the possible solution x=5


-1%2F%280%29=%28-1%29%2F%280%29 Combine like terms. Since dividing by zero is NOT defined, this means that x=5 is NOT a solution.


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Answer:


So there are no solutions.