Question

Solve the rational equation:

5x
x+2
=
3x
x+1:
O A. x = 0, 1/
OB. x= -1
O c. x = 3,1
OD. x = -2,1

Answer 1

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