How do you solve (1/x)=c+(1/b) for x?
multipy both sides by x
1=x[c+(1/b) ]
Now divide both sides by [c+(1/b) ]
Why thank you Mr. bobpursley! 8D
To solve the equation (1/x) = c + (1/b) for x, we need to isolate x on one side of the equation.
Here's how:
Step 1: Start by subtracting (1/b) from both sides of the equation to get rid of the fraction:
(1/x) - (1/b) = c + (1/b) - (1/b)
(1/x) - (1/b) = c + 0
(1/x) - (1/b) = c
Step 2: Find the least common denominator (LCD) of x and b, which is x * b. Multiply both sides of the equation by x * b to eliminate the fractions:
(1/x) * (x * b) - (1/b) * (x * b) = c * (x * b)
b - x = c * (x * b)
Step 3: Distribute c * (x * b) on the right side of the equation:
b - x = c * x * b
Step 4: Move the term with x to the left side by subtracting c * x * b from both sides:
b - x - c * x * b = 0
Step 5: Factor out x on the left side:
-x * (1 + c * b) = -b
Step 6: Divide both sides by -(1 + c * b) to solve for x:
x = -b / (1 + c * b)
That's it! The solution to the equation (1/x) = c + (1/b) for x is x = -b / (1 + c * b).