SOLUTION: Solve the equation by using the LCD. I don't know how to do this one, it look confusing (5) / (x^2+x-6) = (2) + (x-3) / (x-2)

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Question 1031718: Solve the equation by using the LCD.
I don't know how to do this one, it look confusing
(5) / (x^2+x-6) = (2) + (x-3) / (x-2)
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
5/(x^2+x-6) = 2 + (x-3)/(x-2)
x^2+x-6 can be factored.
---

LCD = (x+3)*(x-2)
---

Multiply thru by DEN, the LCD
5 = 2*(x^2+x-6) + (x-3)*(x+3)
5 = 3x^2 + 2x - 21
3x^2 + 2x - 26 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=316 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2.6293981391052, -3.29606480577186. Here's your graph:

==========================




Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Solve the equation by using the LCD.
I don't know how to do this one, it look confusing
(5) / (x^2+x-6) = (2) + (x-3) / (x-2)


 ------- Factoring 1st-fraction denominator: 

5 = 2(x - 2)(x + 3) + (x - 3)(x + 3) ------ Multiplying by LCD, (x - 2)(x + 3)





 



Using the quadratic equation formula, or completing the square should result in:     

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