What is the solution to the equation 1/x - 6/x^2 = -12
a. x= 3/4 or x= -2/3
b. x= 3/4 or x= 2/3
c. x= -3/4 or x= 2/3**
d x= -3/4 or x= -2/3
1/x - 6/x^2 = -12
multiply by x^2 and you have
x-6 = -12x^2
12x^2+x-6 = 0
(3x-2)(4x+3) = 0
x = 2/3 or -3/4
thank you
To find the solution to the equation 1/x - 6/x^2 = -12, we first need to get rid of the denominators.
1. Multiply the entire equation by x^2 to clear the fractions:
(x^2)(1/x) - (x^2)(6/x^2) = (x^2)(-12)
Simplifying, we get:
x - 6 = -12x^2
2. Rearrange the equation to have all terms on one side:
12x^2 + x - 6 = 0
3. Now we can solve this quadratic equation. We can use factoring, completing the square, or the quadratic formula. In this case, let's use factoring:
Factor the quadratic equation to obtain:
(4x - 3)(3x + 2) = 0
This means that either (4x - 3) equals zero or (3x + 2) equals zero.
So, we have two possible solutions:
1) 4x - 3 = 0
4x = 3
x = 3/4
2) 3x + 2 = 0
3x = -2
x = -2/3
Therefore, the solution to the equation 1/x - 6/x^2 = -12 is x = 3/4 or x = -2/3.
The correct answer choice is b. x = 3/4 or x = -2/3.