(3m+15)/(m^2)=(m+1)/(m)

Question

asked Apr 18, 2024 51.8k views

1 Answer

Elad Gasner · Answer 1 · 2024-04-24T01:02:00+0000

Answer:

m1 = 5

m2 = -3

Explanation:

$\frac{3m + 15}{ {m}^(2) } = (m + 1)/(m)$

Use the property of the proportion (cross-multiply):

${m}^(2) (m + 1) = m(3m + 15)$

${m}^(3) + {m}^(2) = 3 {m}^(2) + 15m$

$3 {m}^(2) + 15m - {m}^(2) - {m}^(3) = 0$

$- {m}^(3) + 2 {m}^(2) + 15m = 0$

$m( - {m}^(2) + 2m + 15) = 0$

$m = 0 \: \: \: or \: \: \: - {m}^(2) + 2m + 15 = 0$

Let's solve this quadratic equation:

${ - m}^(2) + 2m + 15 = 0$

a = -1, b = 2, c = 15

$d = {b}^(2) - 4ac = 4 - 4 * ( - 1) * 15 = 4 + 60 = 64 > 0$

m1 = ( - b - √(d) )/(2a) = ( - 2 - 8)/(2 * ( - 1)) = ( - 10)/( - 2) = 5

m2 = ( - b + √(d) )/(2a) = ( - 2 + 8)/(2 * ( - 1)) = (6)/( - 2) = - 3