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. $\(\frac\)53$
• D. $\(\frac\)13$

Answer: (A)

Verified step by step guidance

1. Rewrite the division of fractions as multiplication by the reciprocal. The original expression is: \[\frac{5p+5}{8-10p} \div \frac{3p+3}{2(8-10p)}\] This becomes: \[\frac{5p+5}{8-10p} \times \frac{2(8-10p)}{3p+3}\]
2. Factor common terms in the numerators and denominators where possible. Notice that: - \$5p + 5\( can be factored as \)5(p + 1)$ - \$3p + 3\( can be factored as \)3(p + 1)$ - \$8 - 10p\( can be factored as \)2(4 - 5p)$
3. Substitute the factored forms back into the expression: \[\frac{5(p+1)}{2(4-5p)} \times \frac{2 \cdot 2(4-5p)}{3(p+1)}\]
4. Cancel out common factors that appear in both numerator and denominator: - The factor \((p+1)\) appears in numerator and denominator - The factor \$2(4-5p)$ appears in numerator and denominator After canceling, simplify the remaining numerical coefficients.
5. Multiply the remaining factors to write the quotient in simplest form. This will give you a simplified fraction with numbers only.