Answer:
To solve the equation (5/x) - 2 = 2/(x+3), you can follow these steps:
Clear the denominators by multiplying both sides of the equation by the least common multiple (LCM) of x and (x+3). The LCM of x and (x+3) is x(x+3), so:
(5/x) * x(x+3) - 2x(x+3) = 2/(x+3) * x(x+3)
Simplify by cancelling out the factors:
5(x+3) - 2x(x+3) = 2x
Expand the brackets and simplify:
5x + 15 - 2x^2 - 6x = 2x
Rearrange the terms:
2x^2 + 11x + 15 = 0
Factor the quadratic equation:
(2x + 5)(x + 3) = 0
Use the zero product property and solve for x:
2x + 5 = 0 or x + 3 = 0
If 2x + 5 = 0, then 2x = -5 and x = -5/2.
If x + 3 = 0, then x = -3.
So the solution to the equation (5/x) - 2 = 2/(x+3) is x = -5/2 or x = -3.