Question

Solve the following equation by using formula :

`(4)/(3) - 3 = (5)/(2x + 3), x ≠ 0, -(3)/(2)`

Answer 1

`(4)/(3) - 3 = (5)/(2x + 3), x ≠ 0, -(3)/(2)`

⇒ `(4 - 3x)/x = (5)/(2x + 3)`

⇒ (4 – 3x)(2x + 3) = 5x
⇒ 8x + 12 – 6x² – 9x – 5x = 0
⇒ –6x² – 6x + 12 = 0
⇒ x² + x – 2 = 0
⇒ x² + 2x – x – 2 = 0
⇒ x(x + 2) –1(x + 2) = 0
⇒ (x + 2)(x – 1) = 0
Either x + 2 = 0, 
then x = –2
or
x – 1 = 0,
then x = 1
∴ x = 1, –2.