SOLUTION: solve: 9/x-5 -1=8/x+5

Question 94432: solve:
9/x-5 -1=8/x+5

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Multiply by the LCD

Distribute and simplify

Distribute again

Foil

Distribute the negative

Get all terms to one side

Combine like terms

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-1, b=1, and c=110

Square 1 to get 1

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Notice when we graph , we get:

and we can see that the roots are and . This verifies our answer

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Check:
Let's check the solution x=-10

Start with the given equation

Plug in x=-10

Simplify the denominators

Reduce

Rewrite -1 as

Combine the fractions. Since the two sides of the equation are equal, this verifies the solution x=-10

Let's check the solution x=11

Start with the given equation

Plug in x=11

Simplify the denominators

Reduce

Rewrite -1 as

Combine the fractions. Since the two sides of the equation are equal, this verifies the solution x=11
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