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

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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) About Me  (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...
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
For your equation a=1 b=-4 c=-2
So just substitute the variables...
Remember (-b) means OPPOSITE of the value of b.
So...
x+=+%284+%2B-+sqrt%28+-4%5E2-4%2A1%2A-2+%29%29%2F%282%2A1%29+
Then simplify...
x+=+%284+%2B-+sqrt%28+16%2B8+%29%29%2F%282%29+
Then...
x+=+%284+%2B-+sqrt%28+24+%29%29%2F%282%29+
Simplify the square root of 24 as...
x+=+%284+%2B-+2%2Asqrt%28+6+%29%29%2F%282%29+
Now factor the numerator then cancel...
x+=+2%282+%2B-+1%29%2Asqrt%28+6+%29%2F%282%29+
The 2's cancel...
x+=+2+%2B-+sqrt%28+6+%29
So the final answer is the solution set...
x+=+2+%2B+sqrt%28+6+%29,x+=+2+-+sqrt%28+6+%29
I hope this helps!
Good Luck!
Let me know if you have any other questions!

Answer by checkley71(8403) About Me  (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