SOLUTION: Solve and check all proposed solutions. {{{(x-4)/(x+1)-10/(x^2-1)=0}}}

Question 150026: Solve and check all proposed solutions.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Factor to get

Notice how the LCD is

Multiply both sides by the LCD to clear the fractions.

Distribute. Notice how the denominators cancel.

Simplify

Multiply the terms on the right side to get 0

FOIL

Combine like terms.

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

Rewrite as

Add to 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 answers are or

However, we need to check them first.

Check:

Let's test the first solution

Start with the given equation.

Plug in .

Square 6 to get 36

Combine like terms.

Multiply by

Combine the fractions.

Reduce. Since the equation is true, this means that is a solution.

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

Let's test the second solution

Start with the given equation.

Plug in .

Square -1 to get 1

Combine like terms.
Since division by zero is undefined, this means that is not a solution.

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

Answer:

So the solution to is

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