SOLUTION: Given that 3/(x+1)-5/(y-2) = 1/(z-3), find a simplified expression for x.

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Question 1150757: Given that 3/(x+1)-5/(y-2) = 1/(z-3), find a simplified expression for x.
Found 2 solutions by VFBundy, MathTherapy:
Answer by VFBundy(438) About Me  (Show Source):
Answer by MathTherapy(10557) About Me  (Show Source):
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Given that 3/(x+1)-5/(y-2) = 1/(z-3), find a simplified expression for x. 
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3(y - 2)(z - 3) - 5(x + 1)(z - 3) = (x + 1)(y - 2) ------ Multiplying by LCD, (x + 1)(y - 2)(z - 3)

3(yz - 3y - 2z + 6) - 5(xz - 3x + z - 3) = (xy - 2x + y - 2)

3yz - 9y - 6z + 18 - 5xz + 15x - 5z + 15 = xy - 2x + y - 2

 - 5xz + 15x - xy + 2x = y - 2 - 3yz + 9y + 6z - 18 + 5z - 15

 - 5xz + 17x - xy = 10y - 3yz + 11z - 35

x(- 5z + 17 - y) = 10y - 3yz + 11z - 35