Simplify rt= 1/[(1/r1)+ (1/r2)]
That looks like the formula for the "total" resistance, rt, of two resistors in parallel, r1 and r2. The t, 1 and 2 are subscripts.
It cannot be made much simpler than that, but it can be rewritten
1/rt = 1/r1 + 1/r2
which is a bit more compact and easier to remember.
To simplify the expression 1/[(1/r1) + (1/r2)], we need to find the common denominator and combine the fractions.
The common denominator of (1/r1) and (1/r2) is r1*r2. We can rewrite the expression as follows:
1/[(r2/r1*r2) + (r1/r1*r2)]
To add the fractions, we need the same denominator. The denominator is already r1*r2, so we can combine the numerators:
1/[ (r2 + r1) / (r1*r2) ]
Now, we can flip the numerator and denominator, which is equivalent to dividing by the fraction:
(r1*r2) / (r2 + r1)
Therefore, the simplified expression for rt is (r1*r2) / (r2 + r1).
To simplify the expression, we can start by finding a common denominator. The denominators for both terms are r1 and r2, so we can multiply the first term by r2/r2 and the second term by r1/r1.
rt = 1/[(1/r1) + (1/r2)]
Since we want a common denominator, we can multiply both the numerator and denominator of the first term by r2/r2:
rt = (r2/r2) / [(1/r1)*(r2/r2) + (1/r2)]
Simplifying further:
rt = (r2)/(r1r2/r2 + r2/r2)
rt = (r2)/(r2/r1 + 1)
Next, we need to simplify the fraction by finding a common denominator:
rt = (r2)/[(r2/r1) + 1]
Since we want a common denominator, we can multiply both the numerator and denominator of the first term by r1/r1:
rt = (r2*r1)/(r1*(r2/r1) + r1)
rt = (r1r2)/(r2 + r1)
So, the simplified expression for rt is (r1r2)/(r2 + r1).