Question

find the roots of (1/x+4)-(1/x-7)=11/30​

Answer 1

given:-

(1/x+4) - (1/x-7) = 11/30

find:-

roots

solution:-

(x - 7) -(x+4) / (x+4)×(x-7) = 11/30

( x - 7 - x - 4 ) / (x +4)×(x-7) = 11/30

-11 / (x + 4)×(x-7) = 11/ 30

-11 / x^2 - 7x + 4x - 28 = 11/30

-11 / x^2 - 3x - 28 = 11/30

( x^2 - 3x -28 )× 11 = -( 30× 11)

(x^2 - 3x - 28)×11 / 11 = - 30

x^2 - 3x - 28 = - 30

x^2 - 3x - 28 + 30 = 0

x^2 - 3x + 2 =0

x^2- 2x - x + 2 = 0

x(x - 2) -1 ( x - 2) = 0

(x-2)(x-1) = 0

hence; factors are (x - 2);(x - 1)