Question

सोपे रूप द्या.

`(a^3 - 27)/(5a^2 - 16a + 3) ÷ (a^2 + 3a + 9)/(25a^2 - 1)`

Answer 1

आपणांस माहीत आहे की,

a² − b² = (a + b) (a − b)

a³ − b³ = (a − b)(a² + ab + b²)

`(a^3 - 27)/(5a^2 - 16a + 3) ÷ (a^2 + 3a + 9)/(25a^2 - 1)`

= `((a)^3 - (3)^3)/(5a^2 - 15a - a + 3) ÷ (a^2 + 3a + 9)/((5a^2) - (1)^2)`

= `((a - 3){(a)^2 + (a) xx (3) + (3)^2})/(5a(a - 3) - 1 (a - 3)) ÷ (a^2 + 3a + 9)/((5a + 1)(5a - 1))`

= `((a - 3)(a^2 + 3a + 9))/((5a - 1)(a - 3)) ÷ (a^2 + 3a + 9)/((5a + 1)(5a - 1))`

= `((a - 3)(a^2 + 3a + 9))/((5a - 1)(a - 3)) ÷ ((5a + 1)(5a - 1))/((a^2 + 3a + 9))`

= 5a + 1