1/2 + x/3 = 1) a/4 + b/8 = 2) 2/5 + a/2 = 2) n/10 - m/5 = 3) y/7 - x/3 = 3) 6/25 + a/100 = 4) 2/a + 1/3 = 4) 1/(2a) + 1/(2b) = 5) x/y + 2/3 = 5) 1/(6x) - 1/(6y) = 6) 5/a + 1/b =…

To simplify the expressions you've written, we'll combine like terms and find common denominators where necessary. Here are the solutions to each equation step-by-step:

1. 1/2 + x/3
   • Common denominator: 6
   • \(\frac{3}{6} + \frac{2x}{6} = \frac{3 + 2x}{6}\)

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1. a/4 + b/8
   • Common denominator: 8
   • \(\frac{2a}{8} + \frac{b}{8} = \frac{2a + b}{8}\)

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2. 2/5 + a/2
   • Common denominator: 10
   • \(\frac{4}{10} + \frac{5a}{10} = \frac{4 + 5a}{10}\)

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2. n/10 - m/5
   • Common denominator: 10
   • \(\frac{n}{10} - \frac{2m}{10} = \frac{n - 2m}{10}\)

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3. y/7 - x/3
   • Common denominator: 21
   • \(\frac{3y}{21} - \frac{7x}{21} = \frac{3y - 7x}{21}\)

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3. 6/25 + a/100
   • Common denominator: 100
   • \(\frac{24}{100} + \frac{a}{100} = \frac{24 + a}{100}\)

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4. 2/a + 1/3
   • Common denominator: 3a
   • \(\frac{6}{3a} + \frac{a}{3a} = \frac{6 + a}{3a}\)

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4. 1/(2a) + 1/(2b)
   • Common denominator: 2ab
   • \(\frac{b}{2ab} + \frac{a}{2ab} = \frac{a + b}{2ab}\)

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5. x/y + 2/3
   • Common denominator: 3y
   • \(\frac{3x}{3y} + \frac{2y}{3y} = \frac{3x + 2y}{3y}\)

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5. 1/(6x) - 1/(6y)
   • Common denominator: 6xy
   • \(\frac{y}{6xy} - \frac{x}{6xy} = \frac{y - x}{6xy}\)

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6. 5/a + 1/b
   • Common denominator: ab
   • \(\frac{5b}{ab} + \frac{a}{ab} = \frac{5b + a}{ab}\)

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6. 3/(5c) - 2/(15c)
   • Common denominator: 15c
   • \(\frac{9}{15c} - \frac{2}{15c} = \frac{7}{15c}\)

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7. c/7 - 2/a
   • Common denominator: 7a
   • \(\frac{ac}{7a} - \frac{14}{7a} = \frac{ac - 14}{7a}\)

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7. x/(3a) + (3x)/(6a)
   • Common denominator: 6a
   • \(\frac{2x}{6a} + \frac{3x}{6a} = \frac{5x}{6a}\)

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8. 8/b - a/c
   • Common denominator: bc
   • \(\frac{8c}{bc} - \frac{ab}{bc} = \frac{8c - ab}{bc}\)

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8. a/(28m) - a/(7m)
   • Common denominator: 28m
   • \(\frac{a}{28m} - \frac{4a}{28m} = \frac{-3a}{28m}\)

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9. (ab)/x - y/3
   • Common denominator: 3x
   • \(\frac{3ab}{3x} - \frac{xy}{3x} = \frac{3ab - xy}{3x}\)

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9. b/(10x) + a/(15x)
   • Common denominator: 30x
   • \(\frac{3b}{30x} + \frac{2a}{30x} = \frac{3b + 2a}{30x}\)

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10. (3x)/a + (2y)/b

• Common denominator: ab
• \(\frac{3bx}{ab} + \frac{2ay}{ab} = \frac{3bx + 2ay}{ab}\)

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10. (5x)/(12a) - (2y)/(9a)

• Common denominator: 36a
• \(\frac{15x}{36a} - \frac{8y}{36a} = \frac{15x - 8y}{36a}\)

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Those are the simplified forms for each of the equations you've provided! If you need any further assistance or explanations, feel free to ask.