Which expression represents the sum of the following?
(5)/ (2t + 1) + (-1) / (4t^2 + 4t + 1)
a) 10t + 4 / (2t + 1)^2
b) 4 / (2t + 1)^3
c) 4 / 4t^2 + 6t + 2
d) 10t + 1 / (2t + 1)^2
5/(2t + 1)] - 1/(4t^2+4t+1)]
= [5(2t +1)-1]/(2t+1)^2
= (10t +4)/(2t+1)^2
(a) is correct if you add parentheses around (2t+4). Otherwise (a) is ambiguous
thanks drwls
To find the sum of the expressions (5)/(2t + 1) + (-1)/(4t^2 + 4t + 1), we need to find a common denominator for the two fractions.
The denominators are (2t + 1) and (4t^2 + 4t + 1). To find the common denominator, we can multiply the two denominators together.
The common denominator is (2t + 1)(4t^2 + 4t + 1).
Now, we can multiply the first fraction by (4t^2 + 4t + 1) and the second fraction by (2t + 1):
[(5)(4t^2 + 4t + 1)] / [(2t + 1)(4t^2 + 4t + 1)] + [(-1)(2t + 1)] / [(2t + 1)(4t^2 + 4t + 1)]
Simplifying each fraction:
(20t^2 + 20t + 5) / [(2t + 1)(4t^2 + 4t + 1)] + (-2t - 1) / [(2t + 1)(4t^2 + 4t + 1)]
Now, we can combine the two fractions with the same denominator:
(20t^2 + 20t + 5 - 2t - 1) / [(2t + 1)(4t^2 + 4t + 1)]
Simplifying the numerator:
(20t^2 + 18t + 4) / [(2t + 1)(4t^2 + 4t + 1)]
Now, we can check which answer choice matches this expression:
a) 10t + 4 / (2t + 1)^2
b) 4 / (2t + 1)^3
c) 4 / 4t^2 + 6t + 2
d) 10t + 1 / (2t + 1)^2
Comparing the expression we found with the answer choices, the correct choice is d) 10t + 1 / (2t + 1)^2.