Question

Solve the following equation by using formula :

`(x + 1)/(x + 3) = (3x + 2)/(2x + 3)`

Answer 1

`(x + 1)/(x + 3) = (3x + 2)/(2x + 3)`

(x + 1) (2x + 3) = (3x + 2) (x + 3)
⇒ 2x² + 3x + 2x + 3 = 3x² + 9x + 2x + 6
⇒ 2x² + 5x + 3 - 3x² - 11x - 6 = 0
⇒ -x² - 6x - 3 = 0
⇒ x² + 6x + 3 = 0
Here a = 1, b = 6, c = 3
D = b² - 4ac
= (6)² - 4 x 1 x 3
= 36 - 12
= 24
∵ x = `(-b ± sqrt("D"))/(2a)`

= `(-6 ± sqrt(24))/(2 xx 1)`

= `(6 ± sqrt(4 xx 6))/(2)`

= `(-6 ± 2sqrt(6))/(2)`
= `-3 ± sqrt(6)`
∴ `x_1 = -3 + sqrt(6), x_2 = -3 - sqrt(6)`
Hence x = `-3 + sqrt(6), -3 - sqrt(6)`.