Pregunta
3. Express as a single fraction \( \frac{v+3}{2}+\frac{2 v+1}{5} \)
Ask by Ramirez Dawson. in South Africa
Feb 24,2025
Solución de inteligencia artificial de Upstudy
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The single fraction is \( \frac{9v + 17}{10} \).
Solución
To combine the fractions into a single fraction, first identify the common denominator. The denominators are 2 and 5, and the least common denominator is 10.
Now rewrite each fraction with the denominator 10:
(v + 3)/2 = [5(v + 3)]/10 = (5v + 15)/10
(2v + 1)/5 = [2(2v + 1)]/10 = (4v + 2)/10
Now add the two fractions:
(5v + 15)/10 + (4v + 2)/10 = [5v + 15 + 4v + 2] / 10
= (9v + 17)/10
Thus, the expression as a single fraction is (9v + 17)/10.
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To combine the fractions \( \frac{v+3}{2}+\frac{2v+1}{5} \) into a single fraction, we first need to find a common denominator. The denominators are 2 and 5, and the least common multiple is 10. Now, we convert each fraction: \[ \frac{v+3}{2} = \frac{(v+3) \cdot 5}{2 \cdot 5} = \frac{5(v+3)}{10} = \frac{5v + 15}{10} \] \[ \frac{2v+1}{5} = \frac{(2v+1) \cdot 2}{5 \cdot 2} = \frac{2(2v+1)}{10} = \frac{4v + 2}{10} \] Now, we can add the two fractions: \[ \frac{5v + 15}{10} + \frac{4v + 2}{10} = \frac{(5v + 15) + (4v + 2)}{10} = \frac{9v + 17}{10} \] Thus, the expression as a single fraction is: \[ \frac{9v + 17}{10} \]
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