Question

1,6/n+6=3/5n n-?????​

Answer 1

Ответ:

$\frac{1.6}{n} + 6 = \frac{3}{5n} \\ \frac{ \frac{8}{5} }{n} + 6 = \frac{3}{5n} \\ \frac{8}{5n} - \frac{3}{5n} - 6 \\ \frac{5}{5n} = - 6 \\ 1 = - 6n \\ n = - \frac{1}{6}$

Answer 2

To solve for the value of 'n' in the equation:

1 + 6/(n + 6) = 3/(5n)

You can follow these steps:

Step 1: Get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 5n(n + 6):

5n(n + 6) * [1 + 6/(n + 6)] = 5n(n + 6) * [3/(5n)]

This will cancel out the fractions:

5n(n + 6) * 1 + 5n(n + 6) * [6/(n + 6)] = 3

Step 2: Distribute the terms on both sides of the equation:

5n(n + 6) + 5n * 6 = 3

Step 3: Expand and simplify further:

5n^2 + 30n + 30n = 3

Step 4: Combine like terms:

5n^2 + 60n = 3

Step 5: Move all terms to one side of the equation to set it to zero:

5n^2 + 60n - 3 = 0

Step 6: To solve this quadratic equation, you can use the quadratic formula:

n = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 5, b = 60, and c = -3. Plug these values into the quadratic formula:

n = (-60 ± √(60² - 4 * 5 * (-3))) / (2 * 5)

n = (-60 ± √(3600 + 60)) / 10

n = (-60 ± √3660) / 10

Now, you can calculate the two possible solutions:

n₁ = (-60 + √3660) / 10 ≈ 1.77 (rounded to two decimal places)

n₂ = (-60 - √3660) / 10 ≈ -11.77 (rounded to two decimal places)

So, the two possible values for 'n' are approximately 1.77 and -11.77.