Question

roots of the equation​

Answer 1

Answer:

x=1,2

Step-by-step explanation:

$\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30} \\ \frac{(x - 7) - (x + 4)}{(x + 4)(x - 7)} = \frac{11}{30} \\ \frac{x - 7 - x - 4}{ {x}^{2} - 7x + 4x - 28} = \frac{11}{30} \\ \frac{ - 11}{ {x}^{2} - 3x - 28 } = \frac{11}{30 } \\ 11 {x}^{2} - 33x - 308 = - 330 \\ 11 {x}^{2} - 33x + 22 = 0 \\ \div \: by \: 11 \\ {x}^{2} - 3x + 2 = 0 \\ {x}^{2} - 2x - x + 2 = 0 \\ x(x - 2) - 1(x - 2) = 0 \\ (x - 1)( x - 2) = 0 \\ x = 1 \: and \: 2$

Answer 2

A N S W E R :

x = 1 or 2

E X P L A N A T I O N :

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

By taking LCM of the LHS,

=> [(x-7) - (x+4)]/(x+4)(x-7) = 11/30

=> (x-7-x-4)/(x²-7x+4x-28) = 11/30

=> (-11)/(x²-3x-28) = 11/30

By cross multiplying,

=> 30(-11) = 11(x²-3x-28)

=> -330 = 11(x²-3x-28)

=> x²-3x-28 = -330/11

=> x²-3x-28 = -30

=> x²-3x-28+30 = 0

=> x²-3x+2 = 0

By splitting middle term,

=> x²-2x-x+2 = 0

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

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

=> (x-1) = 0 ⠀⠀⠀⠀⠀⠀(x-2) = 0

=> x = 1 ⠀⠀⠀⠀⠀⠀⠀⠀x = 2

∴ 1 and 2 are the roots of the given expression.