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

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) (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
-----------------
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) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Cross multiply

FOIL

Distribute

Add x to both sides. Subtract 5 from both sides.

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible solution is

However, we must check the answer.

-------------------------

Check:

Start with the given equation

Plug in the possible solution

Combine like terms. Since dividing by zero is NOT defined, this means that is NOT a solution.

============================================

Answer:

So there are no solutions.
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