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Answer:

See below ↓

Step-by-step explanation:

Problem

  • [tex]\frac{5x}{x+7} + \frac{7}{x}[/tex]

Work

  • [tex]\frac{5x(x)+7(x+7)}{x(x+7)}[/tex]
  • [tex]\frac{5x^{2} +7x+49}{x(x+7)}[/tex]
  • The student's mistake was that instead of taking x(x + 7) as the LCM (Least Common Multiple), he took x + 7, which is not possible in this case

Solution

  • [tex]\frac{5x^{2} +7x+49}{x(x+7)}[/tex]