I forget how to do math 1/6-1/x=4/3x^2?

Question

I forget how to do this...

Answer 1

First get a common denominator on the left so that you can combine the fractions... multiply the first fraction by x/x and the second by 6/6.  Now you have the common denominator of 6x:

x/6x - 6/6x = 4/3x²

Combine the fraction on the left by subtracting:

(x - 6) / 6x = 4 / 3x²

Cross multiply:

3x² (x - 6) = 4 * 6x

Simplify:

3x²(x - 6) = 24x

3x^3 - 18x² = 24x

Subtract 24x from both sides to get 0 on one side:

3x^3 - 18x² - 24x = 0

Now factor completely:

3x(x² - 6x - 8) = 0

3x(x - 2)(x - 4) = 0

Break it into parts for your solution:

3x = 0

or

x - 2 = 0

or

x - 4 = 0

Then solve:

x = 0/3 = 0

or

x = 0 + 2 = 2

or

x = 0 + 4 = 4

Possible solutions:

x = 0 or x = 2 or x = 4

However, notice that x = 0 can't be a solution because you would have division by 0.

Answer:

x = 2 or x = 4