If x = -5, what is the value of `((x^2 -1)/(x+1))` ?

Options

A. `-6`
B. `-4`
C. `4`
D. `5 4/5`

Answer

To solve the expression \(\frac{x^2 - 1}{x + 1}\) when \(x = -5\), we can follow these steps:

### Step 1: Substitute the value of \(x\)
We start by substituting \(-5\) into the expression:

\[ \frac{(-5)^2 - 1}{-5 + 1} \]

### Step 2: Calculate \((-5)^2\)
Next, we calculate \((-5)^2\):

\[ (-5)^2 = 25 \]

### Step 3: Substitute back into the expression
Now, we substitute \(25\) back into the expression:

\[ \frac{25 - 1}{-5 + 1} \]

### Step 4: Simplify the numerator
Now, simplify the numerator \(25 - 1\):

\[ 25 - 1 = 24 \]

### Step 5: Simplify the denominator
Next, simplify the denominator \(-5 + 1\):

\[ -5 + 1 = -4 \]

### Step 6: Form the new fraction
Now we can form the new fraction:

\[ \frac{24}{-4} \]

### Step 7: Simplify the fraction
Finally, we simplify the fraction:

\[ \frac{24}{-4} = -6 \]

### Final Answer
Thus, the value of \(\frac{x^2 - 1}{x + 1}\) when \(x = -5\) is \(-6\).

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