Question

1/x+4- 1/x-7=11/30‚x= - 4,7​

Answer 1

Answer:

$\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30} \\ \frac{(x - 7) - (x + 4)}{(x + 4)(x - 7)} = \frac{11}{30} \\ \frac{ \cancel x - 7 \cancel{ - x} - 4}{ {x}^{2} - 7x + 4x - 28 } = \frac{11}{30} \\ \frac{ - 11}{ {x}^{2} - 3x - 28 } = \frac{11}{30} \\ - 11 \times 30 = 11( {x}^{2} - 3x - 28) \\ - 330 = 11 {x}^{2} - 33x - 308 \\ - 330 + 308 = 11 {x}^{2} - 33x \\ - 22 = 11 {x}^{2} - 33x \\ 11 {x}^{2} - 33x + 22 = 0 \\ 11( {x}^{2} - 3x + 2) = 0 \\ {x}^{2} - 3x + 2 = 0 \\ {x}^{2} - 2x - x + 2 = 0 \\ x(x - 2) - 1(x - 2) = 0 \\ (x - 2)(x - 1) = 0 \\ x - 2 = 0 \: \: \: or \: \: \: x - 1 = 0 \\ \boxed{ x = \underline{ \underline{ \bf 2}} \: \: \: or \: \: \: x = \underline{ \underline{ \bf 1}}}$