SOLUTION: find all real or imaginary solutions to each equation. x-1/x+2 = 2x-3/x+4

Question 96449: find all real or imaginary solutions to each equation.
x-1/x+2 = 2x-3/x+4

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Multiply both sides by the LCD

Notice the LCD eliminates the denominators

Simplify

Foil both sides

Get all terms to one side and 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=-2, and c=-2

Negate -2 to get 2

Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because .)

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

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our solutions are:
or

Notice when we graph , we get:

when we use the root finder feature on a calculator, we find that and .So this verifies our answer
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