solve the rational equation
4/x-2= x/12
To solve the rational equation 4/(x-2) = x/12, we can start by cross-multiplying, which means multiplying both sides of the equation by the denominators of the fractions involved. This will help eliminate the fractions and simplify the equation.
Let's go through the steps:
1. Cross-multiply:
4 * 12 = x * (x - 2)
2. Simplify:
48 = x^2 - 2x
3. Rearrange the equation to set it equal to zero:
x^2 - 2x - 48 = 0
Now, we have a quadratic equation. Let's use factoring or the quadratic formula to solve it.
4. Factoring:
(x - 8)(x + 6) = 0
Setting each factor equal to zero:
x - 8 = 0 or x + 6 = 0
Solving for x:
x = 8 or x = -6
So, the two possible solutions for the given rational equation are x = 8 and x = -6.