Solve each equation for the specified variable. (Assume all de...

Question

Solve each equation for the specified variable. (Assume all denominators are nonzero.) 1/R=1/r_1 + 1/r_2, for R

Accepted Answer

Hey, everyone here we are asked to solve for I in the following equation, two divided by I is equal to one divided by M minus one divided by N. So our first step here in solving for I is to combine the fractions on the right side of our equation. So looking at these fractions, again, we have one divide By M -1 divided by N. Well, to combine these fractions, we need to get common denominators. So starting with our first fraction, we need to multiply the numerator and the denominator by the value of the other denominator. So we multiply the numerator and the denominator of our first fraction by N. And then we repeat a similar process for our second fraction. But we multiply the numerator and the denominator by the value of the denominator of the first fraction. So we just have one divided by N times M divided by M. So now we just need to simplify our fractions and we have N divided by M times N minus M divided by M times N. And now we can just simplify our fractions here by combining the numerator. Since we have found our common denominators. So doing this, we now have the quantity of N minus M all divided by M times N. And now we can just substitute in the, this new expression for our two fractions from our original equation. So we now have two divided by I is equal to N minus M all divided by M times N. So now we see that on the left side of our equation, we have I in the denominator. Well, we want I in the numerator. So that means we just need to take the reciprocal of both sides of our equation. So we will instead have I divided by two is equal to M times N divided by N minus M. And now we just need to get rid of this denominator of I, which is two. So we just need to multiply both sides of our equation by the denominator which is two. So doing this and simplifying we have I is equal to two times M times N all divided by N minus M. And with this, we have solved for I from our original equation. So this is our final equation which leaves us with answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time.

Solve each equation for the specified variable. (Assume all denominators are nonzero.) 1/R=1/r_1 + 1/r_2, for R

Key Concepts

Solving Equations for a Specific Variable

Working with Rational Expressions

Reciprocals and Their Properties

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