Question

if (4x^2 + xy) : (3xy - y^2) = 12 :5, find (x +2y) : ( 2x + y)

Answer 1

Answer:

11/10   & 14/13

Step-by-step explanation:

if (4x^2 + xy) : (3xy - y^2) = 12 :5, find (x +2y) : ( 2x + y)

Let say

x = ay

then

(4x² + xy)/(3xy - y²)  = 12/5

will be

(4a²y² + ay²)/(3ay² - y²) = 12/5

=> 20a²y² + 5ay² = 36ay² - 12y²

dividing by y² both sides

=> 20a² + 5a = 36a - 12

=> 20a² -31a + 12 = 0

=> 20a² - 16a - 15a + 12 = 0

=> 4a(5a - 4) - 3(5a -4) = 0

=> (4a -3) (5a -4) = 0

a = 3/4   or a = 4/5

Case 1  a = 3/4

(x + 2y)/(2x + y)

= (3y/4  + 2y)/(2*3y/4  + y)

= (3y + 8y) / (6y + 4y)

= 11y/10y

= 11/10

case 2   a = 4/5

(x + 2y)/(2x + y)

= (4y/5  + 2y)/(2*4y/5  + y)

= (4y + 10y) / (8y + 5y)

= 14y/13y

= 14/13