how do i solve this?
x +(12/x)=12
and
(5/x+4)=4+(3/x-2)
First: multiply both sides of the equation by x. then solve the quadratic.
Second Same technique.
thank-you. i see how to do it now
To solve the first equation, x + (12/x) = 12, you can follow these steps:
Step 1: Get rid of the fraction by multiplying each term by x.
x * x + 12 = 12 * x
x^2 + 12 = 12x
Step 2: Move all the terms to one side to create a quadratic equation.
x^2 - 12x + 12 = 0
Step 3: Solve the quadratic equation using factoring, completing the square, or the quadratic formula.
In this case, factoring might be a little complex, so let's use the quadratic formula. The standard quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -12, and c = 12. Plugging in the values, we get:
x = (-(-12) ± √((-12)^2 - 4*1*12)) / (2*1)
x = (12 ± √(144 - 48)) / 2
x = (12 ± √96) / 2
x = (12 ± 4√6) / 2
Simplifying this further, we get:
x = 6 ± 2√6
So, the solutions to the equation x + (12/x) = 12 are x = 6 + 2√6 and x = 6 - 2√6.
Now, if we move on to the second equation, (5/x + 4) = 4 + (3/x - 2), we can simplify it as follows:
Step 1: Remove the fractions by multiplying each term by x.
x * (5/x + 4) = x * (4 + (3/x - 2))
5 + 4x = 4x + 3 - 2x
Step 2: Combine like terms on both sides of the equation.
4x - 4x + 2x = 3 - 5
2x = -2
Step 3: Solve for x by dividing both sides by 2.
x = -2/2
x = -1
So, the solution to the equation (5/x + 4) = 4 + (3/x - 2) is x = -1.