Questions: Divide. [ (2 x+16)/(8 x-5) div (x+8)/(2 x-8) ] Simplify your answer as much as possible.

Solution Steps

To solve the expression \[ \frac{2x + 16}{8x - 5} \div \frac{x + 8}{2x - 8}, \] we rewrite the division as multiplication by the reciprocal: \[ \frac{2x + 16}{8x - 5} \times \frac{2x - 8}{x + 8}. \]

Next, we factor the numerator and denominator of the resulting expression:

• The numerator \(2x + 16\) can be factored as \(2(x + 8)\).
• The numerator \(2x - 8\) can be factored as \(2(x - 4)\).
• The denominator \(8x - 5\) remains as is.
• The denominator \(x + 8\) remains as is.

Thus, we have: \[ \frac{2(x + 8)}{8x - 5} \times \frac{2(x - 4)}{x + 8}. \]

Now, we can simplify the expression by canceling the common factor \(x + 8\): \[ \frac{2 \cdot 2(x - 4)}{8x - 5} = \frac{4(x - 4)}{8x - 5}. \]

Final Answer