Question

Solve the equation and verify your answer:

((x+1)/(x-4))² = (x+8)/(x-2)

Answer 1

We have,

((x+1)/(x-4))² = (x+8)/(x-2)

(x+1)² / (x-4)² – (x+8) / (x-2) = 0

By taking LCM as (x-4)² (x-2)

((x+1)² (x-2) – (x+8) (x-4)²) / (x-4)² (x-2) = 0

By cross-multiplying we get,

(x+1)² (x-2) – (x+8) (x-4)² = 0

Upon expansion we get,

(x² + 2x + 1) (x-2) – ((x+8) (x² – 8x + 16)) = 0

x³ + 2x² + x – 2x² – 4x – 2 – (x³ – 8x² + 16x + 8x² – 64x + 128) = 0

x³ + 2x² + x – 2x² – 4x – 2 – x³ + 8x² – 16x – 8x² + 64x – 128 = 0

45x – 130 = 0

x = 130/45

= 26/9

Now let us verify the given equation,

((x+1)/(x-4))² = (x+8)/(x-2)

(x+1)² / (x-4)² = (x+8) / (x-2)

By substituting the value of ‘x’ we get,

(26/9 + 1)² / (26/9 – 4)² = (26/9 + 8) / (26/9 – 2)

((26+9)/9)² / ((26-36)/9)² = ((26+72)/9) / ((26-18)/9)

(35/9)² / (-10/9)² = (98/9) / (8/9)

(35/-10)² = (98/8)

(7/2)² = 49/4

49/4 = 49/4

Hence, the given equation is verified.