Final answer:
To solve the rational equation, cross-multiply, expand, simplify, and solve for x. The solutions are x = 0 or x = 1/2.
Step-by-step explanation:
To solve the given rational equation,
5x/(x+2) = 3x/(x+1)
we need to cross-multiply and solve for x.
First, cross-multiply to get:
5x(x+1) = 3x(x+2)
Next, expand and simplify both sides of the equation:
5x^2 + 5x = 3x^2 + 6x
Combine like terms:
2x^2 - x = 0
Factor out an x:
x(2x - 1) = 0
Set each factor equal to zero and solve for x:
x = 0 or 2x - 1 = 0
x = 0 or x = 1/2
Therefore, the solutions to the equation are x = 0 or x = 1/2.
Learn more about Solving rational equations