Question

Solve for x 2(2x-1\x+3)-3(x+3\2x-1)=5

Answer 1

2 [(2x - 1)/(x + 3)] - 3 [(x + 3)/ (2x - 1)] = 5

Put y = (2x - 1)/(x + 3)

Then the given equation is,

2y - 3/y = 5

⇒ 2y² - 5y - 3 = 0

⇒ 2y²- 6y + y - 3 = 0

⇒ 2y (y-3) + 1 (y-3) = 0

(y - 3)(2y + 1) = 0

Therefore, y = 3 or y = -1/2

Now, (2x-1/x+3) = y = 3

⇒(2x-1) / (x+3) = 3

⇒ 2x - 1 = 3x + 9

⇒ x + 10 = 0

⇒x = -10.

Also, (2x-1/x+3) = y = -1/2

⇒ 4x - 2 = -x - 3

⇒ 5x = -1

⇒ x = -1/5

Hope it helps
All the best.