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.