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Class-10»Maths

solve for x:1/x+1+2/x+2=4/x+4

$\frac{1}{x + 1} + \frac{2}{x + 2} = \frac{4}{x + 4} \frac{x + 2 + 2 x + 2}{(x + 1) (x + 2)} = \frac{4}{x + 4} \frac{3 x + 4}{x^{2} + 3 x + 2} = \frac{4}{x + 4} (3 x + 4) (x + 4) = 4 (x^{2} + 3 x + 2) 3 x^{2} + 12 x + 4 x + 16 = 4 x^{2} + 12 x + 8 3 x^{2} - 4 x^{2} + 16 x - 12 x + 16 - 8 = 0 - x^{2} + 4 x + 8 = 0 x^{2} - 4 x - 8 = 0 x = \frac{4 \pm \sqrt{16 + 32}}{2} = \frac{4 \pm \sqrt{48}}{2} x = \frac{4 \pm 4 \sqrt{3}}{2} = 2 \pm 2 \sqrt{3} x = 2 + 2 \sqrt{3}, 2 - 2 \sqrt{3} x = 2 + 2 * 1.732, 2 - 2 * 1.732 x = 5.46, - 1.46$

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