Simplify: `(-1+(7)/(-9))+(11)/(12)`

Answer

To simplify the expression \((-1 + \frac{7}{-9}) + \frac{11}{12}\), we can follow these steps:

### Step 1: Rewrite the expression
We start by rewriting the expression:
\[ (-1 + \frac{7}{-9}) + \frac{11}{12} \]
This can be simplified to:
\[ -1 - \frac{7}{9} + \frac{11}{12} \]

### Step 2: Convert -1 to a fraction
To combine these fractions, we can convert \(-1\) into a fraction with a denominator of \(9\):
\[ -1 = -\frac{9}{9} \]
Now the expression looks like this:
\[ -\frac{9}{9} - \frac{7}{9} + \frac{11}{12} \]

### Step 3: Combine the fractions with the same denominator
Now, we can combine the fractions with the same denominator:
\[ -\frac{9 + 7}{9} + \frac{11}{12} = -\frac{16}{9} + \frac{11}{12} \]

### Step 4: Find the LCM of the denominators
Next, we need to find the least common multiple (LCM) of \(9\) and \(12\). The LCM of \(9\) and \(12\) is \(36\).

### Step 5: Convert each fraction to have the common denominator
Now we convert each fraction to have a denominator of \(36\):
\[ -\frac{16}{9} = -\frac{16 \times 4}{9 \times 4} = -\frac{64}{36} \]
\[ \frac{11}{12} = \frac{11 \times 3}{12 \times 3} = \frac{33}{36} \]

### Step 6: Combine the fractions
Now we can combine the two fractions:
\[ -\frac{64}{36} + \frac{33}{36} = \frac{-64 + 33}{36} = \frac{-31}{36} \]

### Final Result
Thus, the simplified expression is:
\[ -\frac{31}{36} \]

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