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Which of the following expressions is equivalent to (49 r+14)/(42 r+42) ? Choose 1 answer: A) (7r+1)/(6r+3) (B) (7r+2)/(r+1) (C) (49 r+2)/(42 r+6) (D) (7r+2)/(6r+6)

Which of the following expressions is equivalent to 49r+1442r+42 \frac{49 r+14}{42 r+42} ?\newlineChoose 11 answer:\newline(A) 7r+16r+3 \frac{7 r+1}{6 r+3} \newline(B) 7r+2r+1 \frac{7 r+2}{r+1} \newline(C) 49r+242r+6 \frac{49 r+2}{42 r+6} \newline(D) 7r+26r+6 \frac{7 r+2}{6 r+6}

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Q. Which of the following expressions is equivalent to 49r+1442r+42 \frac{49 r+14}{42 r+42} ?\newlineChoose 11 answer:\newline(A) 7r+16r+3 \frac{7 r+1}{6 r+3} \newline(B) 7r+2r+1 \frac{7 r+2}{r+1} \newline(C) 49r+242r+6 \frac{49 r+2}{42 r+6} \newline(D) 7r+26r+6 \frac{7 r+2}{6 r+6}
  1. Factor out common factors: Factor out the common factors in the numerator and the denominator.\newlineThe numerator 49r+1449r + 14 can be factored by taking out the common factor of 77, which gives us 7(7r+2)7(7r + 2).\newlineThe denominator 42r+4242r + 42 can be factored by taking out the common factor of 4242, which gives us 42(r+1)42(r + 1).\newlineSo, (49r+14)/(42r+42)(49r + 14)/(42r + 42) becomes (7(7r+2))/(42(r+1))(7(7r + 2))/(42(r + 1)).
  2. Simplify by canceling common factors: Simplify the expression by canceling out the common factors.\newlineWe can divide both the numerator and the denominator by 77.\newlineThis gives us (7r+2)/(6(r+1))(7r + 2)/(6(r + 1)).
  3. Expand denominator to check: Expand the denominator to check if it matches any of the answer choices.\newlineThe denominator 6(r+1)6(r + 1) expands to 6r+66r + 6.\newlineSo, the simplified expression is (7r+2)/(6r+6)(7r + 2)/(6r + 6).

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