QuestionAugust 25, 2025

Subtract. (x+2)/(2x+6)-(x-3)/(5x+15) Simplify your answer as much as possible. square

Subtract. (x+2)/(2x+6)-(x-3)/(5x+15) Simplify your answer as much as possible. square
Subtract.
(x+2)/(2x+6)-(x-3)/(5x+15)
Simplify your answer as much as possible.
square

Solution
4.1(243 votes)

Answer

\frac{3x + 16}{10(x+3)} Explanation 1. Factor denominators Factor 2x+6 as 2(x+3) and 5x+15 as 5(x+3). 2. Find common denominator The common denominator is 10(x+3). 3. Rewrite fractions with common denominator \frac{x+2}{2(x+3)} = \frac{5(x+2)}{10(x+3)} and \frac{x-3}{5(x+3)} = \frac{2(x-3)}{10(x+3)}. 4. Subtract numerators \frac{5(x+2) - 2(x-3)}{10(x+3)} = \frac{5x + 10 - 2x + 6}{10(x+3)}. 5. Simplify numerator Combine like terms: 3x + 16. 6. Final simplified expression \frac{3x + 16}{10(x+3)}.

Explanation

1. Factor denominators<br /> Factor $2x+6$ as $2(x+3)$ and $5x+15$ as $5(x+3)$.<br />2. Find common denominator<br /> The common denominator is $10(x+3)$.<br />3. Rewrite fractions with common denominator<br /> $\frac{x+2}{2(x+3)} = \frac{5(x+2)}{10(x+3)}$ and $\frac{x-3}{5(x+3)} = \frac{2(x-3)}{10(x+3)}$.<br />4. Subtract numerators<br /> $\frac{5(x+2) - 2(x-3)}{10(x+3)} = \frac{5x + 10 - 2x + 6}{10(x+3)}$.<br />5. Simplify numerator<br /> Combine like terms: $3x + 16$.<br />6. Final simplified expression<br /> $\frac{3x + 16}{10(x+3)}$.
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