use the proporties of operation to add (k+1/3) + 10 (1/2k-1)

Answer 1

To add the two fractions, we need a common denominator.

The common denominator for (k+1)/3 and 10(1/2k-1) is 3(2k-1).

After finding the common denominator, we can rewrite the two fractions as follows:

(k+1)/3 = (2k-1)(k+1)/(2k-1)(3)

10(1/2k-1) = (10)(3)/(2k-1)(3)

Now, we can add the fractions:

((2k-1)(k+1) + (10)(3))/((2k-1)(3))

Expanding the numerator, we get:

(2k² + k - k - 1 + 30)/(3(2k-1))

Combining like terms, we have:

(2k² + 29)/(3(2k-1))

Therefore, the sum of (k+1)/3 and 10(1/2k-1) is (2k² + 29)/(3(2k-1)).