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(5/x) - 2 = 2/x+3 how do i solve this???????​

User Seal
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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.

User Mgutz
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