Add the fractions.

9/19+-10/9

First we need to find the common denominator, which is 171.

9/19 = 81/171
10/9 = 190/171

81/171 + 190/171 = 271/171 = 1 100/171

171

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180

To add fractions, you first need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators.

In this case, the denominators are 19 and 9. The LCM of 19 and 9 is 171.

Once you have the common denominator, you can rewrite the fractions with the same denominator.

9/19 can be rewritten as (9 * 9)/(19 * 9) = 81/171
-10/9 can be rewritten as (-10 * 19)/(9 * 19) = -190/171

Now that both fractions have the same denominator, you can add them together.

81/171 + (-190/171) = (81 - 190)/171 = -109/171

So, the sum of 9/19 and -10/9 is -109/171.