Question

(3n)/(2-n)=(n)/(n+4) Solve the proportion.

Answer 1

n = 0 or n = -5/2

Explanation:

We'd like to solve this equation for n:
`(3n)/(2-n) =(n)/(n+4)`.

Cross-multiply and distribute:

(2 - n) * n = (n + 4) * 3n

2n - n² = 3n² + 12n

Move everything to one side:

3n² + n² + 12n - 2n = 0

4n² + 10n = 0

Factor our 2n:

2n * (2n + 5) = 0

By the Zero Property of Multiplication, either 2n = 0 or 2n + 5 = 0 to make this equation true:

2n = 0 OR 2n + 5 = 0

n = 0/2 = 0 OR 2n = -5 ⇒ n = -5/2

Thus, n = 0 or n = -5/2.

~ an aesthetics lover

Answer 2

n={0; -5/2}

Explanation:

(3n)/(2-n)=(n)/(n+4); n≠2; n≠-4

3n(n+4)=n(2-n)

=> 3n²+12n=2n-n²

4n²+10n=0

2n(2n+5)=0

n=0; n= -5/2