Solve the following equations using the general formula:

Cross multiply

⇒ 5 × (x² – 1) = 4 × (x² + 1)

⇒ 5x² – 5 = 4x² + 4

⇒ 5x² – 5 – 4x² – 4 = 0

⇒ x² – 9 = 0

⇒ x² + 0x – 9 = 0

Comparing equation x² + 0x – 9 = 0 with ax² + bx + c = 0 we get

a = 1, b = 0 and c = – 9

Discriminant (D) = b² – 4ac

⇒ D = 0² – 4(1)(– 9)

⇒ D = 36

D > 0 implies roots are real and distinct and given by

and

Therefore x = 3 and x = – 3