Final answer:
To solve the given rational equation, multiply both sides by the denominator to get rid of the fractions, combine like terms, and solve for the variable. The solution to the equation is x = 13/6.
Step-by-step explanation:
To solve the rational equation 8 - 6 / x = 5 + 1/2, we need to isolate the variable x. Let's begin by multiplying both sides of the equation by x to get rid of the denominator:
x * (8 - 6 / x) = x * (5 + 1/2)
Simplifying both sides:
8x - 6 = 5x + 1/2x
Combining like terms:
8x - 6 = 5x + 0.5
Next, let's get rid of the decimal by multiplying both sides of the equation by 2:
2(8x - 6) = 2(5x + 0.5)
Simplifying:
16x - 12 = 10x + 1
Moving the variables to one side and the constants to the other side:
16x - 10x = 1 + 12
6x = 13
Finally, we can solve for x by dividing both sides by 6:
x = 13/6
Learn more about Solving rational equations