SOLUTION: I am having a problem with solving for real or imaginary solutions. I need clear and direct steps so I can understand this problem. x-1/x+2=2x-3/x+4 What I have so far(not s

Question 37606: I am having a problem with solving for real or imaginary solutions. I need clear and direct steps so I can understand this problem.
x-1/x+2=2x-3/x+4
What I have so far(not so sure it is right),is:
LCD=(x+2)(x+4)
I performed FOIL and got x^2+6x+8
Then I tried to multiply it to each numerator, but got a number with x^3 and so on, which does not seem to work with this type of problem.
Thank you!

Found 2 solutions by junior403, checkley71:
Answer by junior403(76) (Show Source): You can put this solution on YOUR website!
I can understand your frustration!
Let's see if I can help you...
Your LCD (x+2)(x+4) IS correct...
However, there is no need to FOIL it out here.
A simpler way to solve this type of equation is to cross multiply.
so...
(x-1)(x+4) = (x+2)(2x-3)
Then foil...
This way you skip two extra (unnecessary) steps!
x^2+3x-4 = 2x^2-x-6
Then, combine like terms...
Subtract x^2, 3x and -4 from both sides of the equation...
0 = x^2-4x-2
Then factor by using the quadratic equation...

For your equation a=1 b=-4 c=-2
So just substitute the variables...
Remember (-b) means OPPOSITE of the value of b.
So...

Then simplify...

Then...

Simplify the square root of 24 as...

Now factor the numerator then cancel...

The 2's cancel...

So the final answer is the solution set...
,
I hope this helps!
Good Luck!
Let me know if you have any other questions!

Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
WHAT YOU SHOULD BE DOING IS CROSS MULTIPLYING THE TWO FRACTIONS THUS
(X-1)(X+4)=(X+2)(2X-3) NOW WE HAVE X~2+3X-4=2X~2+X-6 OR X~2-2X+2
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