Solve: `(6x^2+\ 13 x-4)/(2x+5)=(12 x^2+5x-2)/(4x+3)`

Explanation

`(6x^2+\ 13 x-4)/(2x+5)=(12 x^2+5x-2)/(4x+3)`
`⇒ (6x^2 + 13x – 4) (4x + 3) = (12x² + 5x – 2) (2x + 5) `
`⇒ (6x^2 + 13x – 4) × 4x + (6x^2 + 13x – 4) × 3 = (12x^2 + 5x – 2) × 2x + (12x^2 + 5x – 2) × 5 `
`⇒ 24x^3 + 52x^2 – 16x + 18x^2 + 39x – 12 = 24x^3 + 10x^2 – 4x + 60x^2 + 25x – 10`
` ⇒ 24x^3 + 70x^2 + 23x – 12 = 24x^3 + 70x^2 + 21x – 10`
`⇒ 24x^3 + 70x^2 + 23x – 24x^3 – 70x^2 – 21x = – 10 + 12`
` ⇒ 2x = 2 `
`⇒ x = 1`