Question

How do you solve `\frac{6}{5} = \frac{2}{n + 5}`?

Answer 1

`-10/3`

Explanation:

• Multiply both sides by the left denominator
  `6/5 * 5 = 2/(n+5) * 5`
  The fives on the left will cancel leaving:
  `6 = 2/(n+5) * 5`

• Multiply both sides by the right denominator
  `6 * (n+5) = 2/(n+5) * 5 * (n+5)`
  The `(n+5)` on the right will cancel leaving:
  `6 * (n+5) = 2 * 5`
  `6 * (n+5) = 10`

• Expand the bracket on the left side by multiplying each term inside the bracket by the number outside
  `6n + 30 = 10`

• Subtract 30 from both sides
  `6n + 30 - 30 = 10 - 30`
  `6n = -20`

• Divide both sides by 6
  `(6n)/6 = -20/6`
  `n = -10/3`