Divide each expression and write the quotient in its simplest form.
$\frac{5p+5}{8-10p}÷\frac{3p+3}{2(8-10p)}$

• A. $\frac{10}{3}$
• B. $\frac{3}{10}$
• C. $\frac{5}{3}$
• D. $\frac{1}{3}$

Answer: (A)

Verified step by step guidance

1. Rewrite the division of fractions as multiplication by the reciprocal. So, change the expression from \(\frac{5p+5}{8-10p} \div \frac{3p+3}{2(8-10p)}\) to \(\frac{5p+5}{8-10p} \times \frac{2(8-10p)}{3p+3}\).
2. Factor all possible expressions in the numerators and denominators. For example, factor \$5p+5\( as \)5(p+1)\( and \)3p+3\( as \)3(p+1)\(. Also, note that \)8-10p$ is common in numerator and denominator.
3. Substitute the factored forms back into the expression: \(\frac{5(p+1)}{8-10p} \times \frac{2(8-10p)}{3(p+1)}\).
4. Cancel out common factors that appear in both numerator and denominator, such as \((p+1)\) and \((8-10p)\), to simplify the expression.
5. Multiply the remaining factors in the numerator and denominator to write the quotient in its simplest form.