Solve for r1 1/r=1/a+1/b

Problem

1/r=1/a+1/b

Solution

1. Identify the variable to solve for. In this context, (r_1) likely refers to the variable r in the provided equation 1/r=1/a+1/b

2. Find a common denominator for the terms on the right side of the equation. The common denominator for a and b is a*b

3. Combine the fractions on the right side by rewriting each term with the common denominator.

1/r=b/(a*b)+a/(a*b)

1/r=(b+a)/(a*b)

4. Take the reciprocal of both sides of the equation to isolate r

r=(a*b)/(b+a)

5. Rearrange the denominator using the commutative property of addition for a standard form.

r=(a*b)/(a+b)

Final Answer

1/r=1/a+1/b⇒r=(a*b)/(a+b)

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