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Question 30011: How do i do 4/x-3 + 2x/x squared - 9 = 1/x+3
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! 4/x-3 + 2x/x squared - 9 = 1/x+3
4/(x-3) + 2x/(x^2-9) = 1/(x+3)----(1)
Observe that (x^2-9) = (x+3)(x-3)
using formula a^2-b^2 = (a+b)(a-b)and here a = x and b = 3
Multliplying (1) through out by (x^2-9)
(divide the lcm of by each of the drs and multiply the answer by the corresponding nr and give the sign given between the terms.
4(x+3)+2x =(x-3)
4x+12+2x=x-3
(4x+2x-x)=-3-12 (grouping like terms, changing sign while changing side)
5x=-15
x =-15/5 = -3
Answer: x =-3 THIS IS WRONG
Why? Because division by zero is not defined(as zero does not have mulitplicative inverse)
Note: If the problem is say like this:
4/(x-3) - 2x/(x^2-9) = 1/(x+3)----(1)
Multliplying (1) through out by (x^2-9)
4(x+3)-2x =(x-3)
4x+12-2x=x-3
(4x-2x-x)=-3-12 (grouping like terms, changing sign while changing side)
x=-15
x =-15
Answer: x =-15
Verification: x = -15 in (1) holds
LHS = -1/12 = RHS
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