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(r^(2)+14 r+49)/(r^(2)+15 r+56) Which expression is equivalent to the given expression, for all r > 0 ? Choose 1 answer: (A) (14 r+49)/(15 r+56) (B) (14+7)/(15+8) (C) (r+7)/(r+8) (D) (49)/(r+56)

r2+14r+49r2+15r+56 \frac{r^{2}+14 r+49}{r^{2}+15 r+56} \newlineWhich expression is equivalent to the given expression, for all r>0 ?\newlineChoose 11 answer:\newline(A) 14r+4915r+56 \frac{14 r+49}{15 r+56} \newline(B) 14+715+8 \frac{14+7}{15+8} \newline(C) r+7r+8 \frac{r+7}{r+8} \newline(D) 49r+56 \frac{49}{r+56}

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Q. r2+14r+49r2+15r+56 \frac{r^{2}+14 r+49}{r^{2}+15 r+56} \newlineWhich expression is equivalent to the given expression, for all r>0 r>0 ?\newlineChoose 11 answer:\newline(A) 14r+4915r+56 \frac{14 r+49}{15 r+56} \newline(B) 14+715+8 \frac{14+7}{15+8} \newline(C) r+7r+8 \frac{r+7}{r+8} \newline(D) 49r+56 \frac{49}{r+56}
  1. Factor Numerator and Denominator: Factor the numerator and denominator.\newlineNumerator: r2+14r+49r^2 + 14r + 49 can be factored as (r+7)(r+7)(r + 7)(r + 7) or (r+7)2(r + 7)^2.\newlineDenominator: r2+15r+56r^2 + 15r + 56 can be factored as (r+7)(r+8)(r + 7)(r + 8).
  2. Write Factored Form: Write the factored form of the expression.\newlineSo, (r2+14r+49)/(r2+15r+56)(r^{2}+14r+49)/(r^{2}+15r+56) becomes ((r+7)(r+7))/((r+7)(r+8))((r + 7)(r + 7))/((r + 7)(r + 8)).
  3. Cancel Common Factor: Cancel out the common factor of (r+7)(r + 7) from the numerator and denominator.\newlineThis leaves us with r+7r+8\frac{r + 7}{r + 8}.
  4. Check Answer Choices: Check the answer choices to see which one matches our simplified expression.\newlineThe correct answer is (C) (r+7)/(r+8)(r+7)/(r+8).

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