Solve for x: x+2/x+5=x/x+6​

Step-by-step explanation:

Given equation

(x + 2)(x – 5)(x – 6)(x + 1) = 144

⇒ (x + 2) (x – 6) (x – 5) (x + 1) = 144

⇒ (x2 – 4x – 12) (x2 – 4x – 5) = 144

Put x2 – 4x = y

Then (y – 12)( y – 5) = 144

⇒ y2 – 17y + 60 – 144 = 0

⇒ y2 – 17y – 84 = 0

⇒ y2 – 21y + 4y – 84 = 0

⇒ y(y – 21) + 4(y – 21) = 0

⇒ (y – 21)(y + 4) = 0

⇒ y – 21 = 0 or y + 4 = 0

⇒ y = 21 or y = - 4

But x2 – 4x = y