Final answer:
To simplify the expression 5/(1/6) + 1/(x+1), multiply 5 by the reciprocal of 1/6 to get 30, find a common denominator, and combine terms. The simplified rational expression is (30x + 31)/(x+1).
Step-by-step explanation:
To simplify the given expression 5/(1/6) + 1/(x+1), we need to identify a common denominator and combine the terms. First, we can rewrite 5/(1/6) as multiplying 5 by the reciprocal of 1/6, which gives us 30.
The next step is to find a common denominator for the two terms, which in this case would be 6(x+1). The expression now looks like 180(x+1)/6(x+1) + 6/6(x+1). Since the denominators are now the same, we can combine the numerators. This leaves us with (180(x+1) + 6)/6(x+1).
Finally, distributing the 180 across (x+1) and then adding 6, we have 180x + 180 + 6. So our simplified expression is (180x + 186)/6(x+1). Further simplifying by common factors, we can divide numerator and denominator by 6, we get (30x + 31)/(x+1), which is our final simplified rational expression.