What is the value of `8/(y^2)-(x^2)/(y)` when =-3 and y=-4 ?

Options

A. `-11/4`
B. `-7/4`
C. `7/4`
D. `11/4`

Answer

To solve the expression \( \frac{8}{y^2} - \frac{x^2}{y} \) when \( x = -3 \) and \( y = -4 \), we will follow these steps:

### Step 1: Substitute the values of \( x \) and \( y \)
We start by substituting \( x = -3 \) and \( y = -4 \) into the expression.

\[ \frac{8}{(-4)^2} - \frac{(-3)^2}{-4} \]

### Step 2: Calculate \( y^2 \) and \( x^2 \)
Next, we calculate \( (-4)^2 \) and \( (-3)^2 \):

\[ (-4)^2 = 16 \quad \text{and} \quad (-3)^2 = 9 \]

### Step 3: Substitute the calculated values back into the expression
Now we substitute these values back into the expression:

\[ \frac{8}{16} - \frac{9}{-4} \]

### Step 4: Simplify the fractions
Now we simplify \( \frac{8}{16} \) and \( \frac{9}{-4} \):

\[ \frac{8}{16} = \frac{1}{2} \quad \text{and} \quad \frac{9}{-4} = -\frac{9}{4} \]

### Step 5: Combine the fractions
Now we combine the two fractions:

\[ \frac{1}{2} - \left(-\frac{9}{4}\right) = \frac{1}{2} + \frac{9}{4} \]

### Step 6: Find a common denominator
The common denominator between 2 and 4 is 4. We convert \( \frac{1}{2} \) to have a denominator of 4:

\[ \frac{1}{2} = \frac{2}{4} \]

### Step 7: Add the fractions
Now we can add the two fractions:

\[ \frac{2}{4} + \frac{9}{4} = \frac{2 + 9}{4} = \frac{11}{4} \]

### Final Answer
Thus, the value of the expression \( \frac{8}{y^2} - \frac{x^2}{y} \) when \( x = -3 \) and \( y = -4 \) is:

\[ \frac{11}{4} \]

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