Solve 1/C=1/C1+1/C2 for C1.
Subtract 1/C2 from each side.
1/C1 = 1/C - 1/C2 = (C2-C)/(C*C2)
Now turn both fractions upside down. This is called "taking the reciprocal of both sides"
C1 = C*C2/(C2 - C) = 1/[(1/C) - (1/C2)]
(C+1)(c2_c+)
Well, to solve this equation for C1, we first need to get rid of those pesky fractions. So let's start by multiplying both sides of the equation by C times C1 times C2. This gives us:
C1 + C2 = C(C2)
Now, let's distribute the C on the right side:
C1 + C2 = C^2 * C2
Next, let's bring all the terms to one side of the equation:
C1 = C^2 * C2 - C2
And finally, let's factor out a C2 from the terms on the right side:
C1 = C2 * (C^2 - 1)
So there you have it! The solution for C1 in terms of C and C2 is C2 times (C^2 - 1). Hope that brings a smile to your face!
To solve the equation 1/C = 1/C1 + 1/C2 for C1, we can follow these steps.
Step 1: Get rid of fractions by finding a common denominator.
In this case, the common denominator is C1 × C2, which means we need to multiply both sides of the equation by C1 × C2.
1/C × C1 × C2 = (1/C1 + 1/C2) × C1 × C2
Simplifying this equation will give us,
(C1 × C2) / C = C1 + (C2 × C1) / C2
Step 2: Simplify the right side of the equation.
Using the distributive property, we can rewrite the equation as follows,
(C1 × C2) / C = C1 + (C1 × C2) / C2
Now, we can find the least common denominator of C and C2, which is C × C2. We multiply both sides of the equation by C × C2 to eliminate the fractions on the right side.
(C1 × C2) / C × C × C2 = C1 × C × C2 + (C1 × C2) / C2 × C × C2
Simplifying this equation will give us,
C1 × C2 × C2 = C1 × C × C2 + C1 × C × C2
Step 3: Simplify the equation.
To simplify the equation further, we combine like terms on the right side of the equation.
C1 × C2 × C2 = C1 × C × C2 + C1 × C × C2
C1 × C2 × C2 = 2C1 × C × C2
Step 4: Solve for C1.
To solve for C1, we isolate it on one side of the equation. We can do this by dividing both sides of the equation by 2C × C2.
C1 × C2 × C2 / (2C × C2) = (2C1 × C × C2) / (2C × C2)
Simplifying this equation will give us,
C1 = C / 2
Therefore, the solution to the equation 1/C = 1/C1 + 1/C2 for C1 is C1 = C / 2.