Solve for each of the variables:
1/x+3 - 2/x-2 = 5/x+3
I guess maybe you mean:
1/(x+3) - 2/(x-2) = 5/(x+3)
multiply by [(x+3)(x-2)]
(x-2) -2(x+3) = 5(x-2)
x - 2 - 2 x - 6 = 5 x - 10
2 = 6 x
x =1/3
would it be 2=6x or -2=6x?
To solve for the variables in the given equation, we need to combine like terms and isolate the variable.
1/x+3 - 2/x-2 = 5/x+3
First, let's obtain a common denominator. The common denominator for x+3 and x-2 is (x+3)(x-2). We can rewrite the equation with the common denominator:
[(x-2)(1)]/[(x+3)(x-2)] - [(x+3)(2)]/[(x+3)(x-2)] = [(x+3)(5)]/[(x+3)(x-2)]
Now, let's simplify the equation:
(x - 2)/[(x + 3)(x - 2)] - (2(x + 3))/[(x + 3)(x - 2)] = (5(x + 3))/[(x + 3)(x - 2)]
Notice that the (x + 3) terms in the numerator and denominator of each fraction cancel out:
(x - 2) - 2(x + 3) = 5(x + 3)
Now we can simplify further:
x - 2 - 2x - 6 = 5x + 15
Combine like terms:
-2x - 8 = 5x + 15
Let's isolate the x term on one side by adding 2x to both sides:
-8 = 7x + 15
Now, subtract 15 from both sides:
-8 - 15 = 7x
-23 = 7x
Finally, divide both sides by 7 to solve for x:
x = -23/7
Therefore, the solution to the equation is x = -23/7.