Question

What expression is equivalent to 8p + 8/-32p + 4?
A. p + 2/-4p + 1
B. 2p + 2/-8p + 1
C. 2p + 2/8p + 1
D. p + 1/-8p + 1

Answer 1

Let's simplify the expression \( \frac{8p + 8}{-32p + 4} \).

First, we can factor both the numerator and the denominator:

1. In the numerator \( 8p + 8 \):
- Factor out 8:
\( 8(p + 1) \)

2. In the denominator \( -32p + 4 \):
- Factor out -4:
\( -4(8p - 1) \)

Now, we can rewrite the expression:

\[
\frac{8(p + 1)}{-4(8p - 1)}
\]

Next, we can simplify this expression. We can cancel out \( 8 \) in the numerator and \( -4 \) in the denominator:

\[
\frac{8}{-4} = -2
\]

So, the expression simplifies to:

\[
-\frac{2(p + 1)}{8p - 1}
\]

This gives us:

\[
-\frac{2p + 2}{8p - 1}
\]

To make this a little cleaner in terms of signs, we can multiply the entire expression by -1 (which doesn’t change the value):

\[
\frac{2p + 2}{-8p + 1}
\]

Now let’s analyze this expression to match it with the provided answer choices.

The expression we reached is equivalent to:

\[
\frac{2(p + 1)}{-8p + 1}
\]

Now looking at the choices, we express:

- The expression can be simplified further into:

\[
\frac{2(p + 1)}{-(8p - 1)} = -\frac{2(p + 1)}{8p - 1}
\]

Thus, upon simplifying each choice (and observing factors), we would find the equivalence.

After checking each option against the simplified structure of the fraction we derived.

Resulting equivalently, we see:

Comparing options carefully:

The final expression can be matched against:

From the problem, you relate the equivalent expression which is obtained is option **B (2p + 2/-8p + 1)**.

Thus, the correct answer is **B.**