SOLUTION: Science and medicine. The combined resistance of two resistors, R1 and R2 in a parallel circuit is given by the formula. Rt= 1/ 1/R1 + 1/R2 Simplify the formula. Please h

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Science and medicine. The combined resistance of two resistors, R1 and R2 in a parallel circuit is given by the formula. Rt= 1/ 1/R1 + 1/R2 Simplify the formula. Please h      Log On


   

Question 78666: Science and medicine. The combined resistance of two resistors, R1 and R2 in a parallel circuit is given by the formula.
Rt= 1/ 1/R1 + 1/R2
Simplify the formula.
Please help me to simplify the formula above.
Note: the denominators are 1/R1 + 1/R2
Thank you for helping me.
sean32485
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
Rt=1%2F%28%281%2FR1%29%2B%281%2FR2%29%29
This is called a "complex fraction." To simplify it, multiply
the numerator and the denominator by the LCD of the fractions
in the denominator, i.e. 1%2FR1 and 1%2FR2. "But wait
a minute," you might say, "those are variables. How do I get an LCD?"
Well think about when you had to add 1%2F3%2B1%2F2. The LCD in this
case is the product of the 3 and 2, or 6. Use the same thinking here
with the variable R1 and R2. The LCD is R1%2AR2. To maintain the
equality of the overall fraction, you need to multiply the numerator
and denomenator of the complex fraction by the same number:
Rt=%28%28R1%2AR2%29%2A1%29%2F%28%28R1%2AR2%29%2A%281%2FR1%2B1%2FR2%29%29
Multiplying this out, you get:
Rt=%28%28R1%2AR2%29%2F%28%28R1%2AR2%29%2FR1%2B%28R1%2AR2%29%2FR2%29%29%29
It is legal to cancel parts of the fraction in the denominator.
Cancelling the R1 and the R2 gives you:
Rt=%28%28R1%2AR2%29%2F%28R2%2BR1%29%29
And you are done.
Good Luck,
tutor_paul@yahoo.com