Question

solve equation 1/x+4 -1/x-7=11/30, x≠ -4,7 for x .​

Answer 1

Step-by-step explanation:

$\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30}$

$\frac{(x - 7) - (x + 4)}{(x + 4)(x - 7)} = \frac{11}{30}$

$\frac{x - 7 - x - 4}{ {x}^{2} - 7x + 4x - 28 } = \frac{11}{30}$

$\frac{ - 11}{ {x}^{2} - 3x - 28 } = \frac{11}{30}$

$11( {x}^{2} - 3x - 28) = 30 \times - 11$

$11( {x}^{2} - 3x -2 8) = - 330$

${x}^{2} - 3x - 28 = \frac{ - 330}{11}$

${x}^{2} - 3x - 28 = - 30$

${x}^{2} - 3x - 28 + 30 = 0$

${x}^{2} - 3x + 2 = 0$

${x}^{2} - (2 + 1)x + 2 = 0$

${x}^{2} - 2x - x + 2 = 0$

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

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

either,

x-2=0

x=2

or,

x-1=0

x=1

The value of x are 1 and 2.