Question

Solve the given quadratic equation 1/(x+4) - 1/(x-7) =11/30 , x≠-4,7​

Answer 1

Answer:

$\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30} i.e \: \frac{x - 7 - x - 4}{ {x}^{2} - 3x - 28 } = \frac{11}{30} . \: so \: - 330 = 11 {x}^{2} - 33x - 308 \: i.e \: 11 {x}^{2} - 33x + 22 = 0 \: i.e \: {x}^{2} - 3x + 2 = 0 \: i.e \: (x - 1)(x - 2) = 0 \: i.e \: x = 1 \: or \: 2 \: ans.$