QuestionAugust 24, 2025

Simplify. Express your answer as a single fraction in simplest form. (8s+10)/(s^2)-7s+12+(s)/(s-4) square

Simplify. Express your answer as a single fraction in simplest form. (8s+10)/(s^2)-7s+12+(s)/(s-4) square
Simplify. Express your answer as a single fraction in simplest form. (8s+10)/(s^2)-7s+12+(s)/(s-4) square

Solution
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Answer

\frac{s^2 + 5s + 10}{(s-3)(s-4)} Explanation 1. Factor the Denominator Factor s^2 - 7s + 12 as (s-3)(s-4). 2. Find a Common Denominator The common denominator is (s-3)(s-4). Rewrite \frac{s}{s-4} as \frac{s(s-3)}{(s-3)(s-4)}. 3. Combine Fractions Combine \frac{8s+10}{(s-3)(s-4)} + \frac{s(s-3)}{(s-3)(s-4)} into a single fraction: \frac{8s+10+s(s-3)}{(s-3)(s-4)}. 4. Simplify the Numerator Expand and simplify the numerator: 8s + 10 + s^2 - 3s = s^2 + 5s + 10. 5. Final Simplification The expression becomes \frac{s^2 + 5s + 10}{(s-3)(s-4)}. This is already in simplest form.

Explanation

1. Factor the Denominator<br /> Factor $s^2 - 7s + 12$ as $(s-3)(s-4)$.<br /><br />2. Find a Common Denominator<br /> The common denominator is $(s-3)(s-4)$. Rewrite $\frac{s}{s-4}$ as $\frac{s(s-3)}{(s-3)(s-4)}$.<br /><br />3. Combine Fractions<br /> Combine $\frac{8s+10}{(s-3)(s-4)} + \frac{s(s-3)}{(s-3)(s-4)}$ into a single fraction: $\frac{8s+10+s(s-3)}{(s-3)(s-4)}$.<br /><br />4. Simplify the Numerator<br /> Expand and simplify the numerator: $8s + 10 + s^2 - 3s = s^2 + 5s + 10$.<br /><br />5. Final Simplification<br /> The expression becomes $\frac{s^2 + 5s + 10}{(s-3)(s-4)}$. This is already in simplest form.
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