SOLUTION: hello, I am having trouble finiding the lcd for this equation. Id appreciate the help on this problem but also tips on how to find it in problems like this. thank you, carla

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Question 643834: hello,
I am having trouble finiding the lcd for this equation. Id appreciate the help on this problem but also tips on how to find it in problems like this.
thank you, carla
x/(2x+2)=-2x/(4x+4)+(2x-3)/(x-4)
so far i know i have to get the lcd for 2x+2,4x+4 and x-4 but since there was that -4 im at a loss, thank you
Found 3 solutions by Alan3354, MathLover1, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x/(2x+2)=-2x/(4x+4)+(2x-3)/(x-4)
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The LCD is not relevant.
You need to solve for x
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If you mean x%2F%282x%2B2%29=-2x%2F%284x%2B4%29%2B%282x-3%29%2F%28x-4%29+
Reduce -2x/(4x+4)
x%2F%282x%2B2%29=-x%2F%282x%2B2%29%2B%282x-3%29%2F%28x-4%29+
Add x/(2x+2)
2x%2F%282x%2B2%29=%282x-3%29%2F%28x-4%29+
Reduce again
x%2F%28x%2B1%29=%282x-3%29%2F%28x-4%29+
Cross multiply
x(x-4) = (x+1)*(2x+3)
x%5E2+-+4x+=+2x%5E2+%2B+5x+%2B+3
x%5E2+%2B+9x+%2B+3+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B9x%2B3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%289%29%5E2-4%2A1%2A3=69.

Discriminant d=69 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+69+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289%29%2Bsqrt%28+69+%29%29%2F2%5C1+=+-0.346688068540963
x%5B2%5D+=+%28-%289%29-sqrt%28+69+%29%29%2F2%5C1+=+-8.65331193145904

Quadratic expression 1x%5E2%2B9x%2B3 can be factored:
1x%5E2%2B9x%2B3+=+%28x--0.346688068540963%29%2A%28x--8.65331193145904%29
Again, the answer is: -0.346688068540963, -8.65331193145904. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B9%2Ax%2B3+%29

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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%282x%2B2%29=-2x%2F%284x%2B4%29%2B%282x-3%29%2F%28x-4%29...first factor out 2 in %282x%2B2%29and 4 in %284x%2B4%29

x%2F2%28x%2B1%29=-2x%2F4%28x%2B1%29%2B%282x-3%29%2F%28x-4%29...right side has denominators 4%28x%2B1%29 and %28x-4%29...their LCD is their product (they have no common factors)



x%2F2%28x%2B1%29=-%282x%5E2-8%2B%282x-3%29%2A%284x%2B4%29%29%2F%284%28x%2B1%29%28x-4%29%29

x%2F2%28x%2B1%29=-%282x%5E2-8%2B8x%5E2%2B8x-12x-12%29%2F%284%28x%2B1%29%28x-4%29%29

x%2F2%28x%2B1%29=-%2810x%5E2-4x-20%29%2F%284%28x%2B1%29%28x-4%29%29

x%2F2%28x%2B1%29=-2%285x%5E2-2x-10%29%2F%284%28x%2B1%29%28x-4%29%29

x%2F2%28x%2B1%29=-cross%282%29%285x%5E2-2x-10%29%2F%28cross%284%292%28x%2B1%29%28x-4%29%29

x%2F2%28x%2B1%29=-%285x%5E2-2x-10%29%2F%282%28x%2B1%29%28x-4%29%29





Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x/(2x+2)=-2x/(4x+4)+(2x-3)/(x-4)
------
Factor:
x/(2(x+1)) = -2x/(4(x+1) + (2x-3)/(x-4)
-------
Multiply thru by lcm = 4(x+1)(x-4)
--------------------
2x(x-4) = (-2x)(x-4) + (2x-3)(4(x+1))
------
2x^2-8x = -2x^2+8x + 4(2x^2-x-3)
----
4x^2-16x = 8x^2-4x - 12
4x^2 + 12x -12 = 0
x^2 + 3x - 3 = 0
---
x = [-3 +- sqrt(9+12)]/2
----
x = [-3+sqrt(21)]/2 or x = [-3-sqrt(21)]/2
========================================
Cheers,
Stan H.