Question

Solve the equation..
$\frac{1}{x + 1} + \frac{2}{x + 2} = \frac{4}{x + 4}$
Step by step... correct answer would be marked as brainlist.(.^_^.)
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Answer 1

Step-by-step explanation:

${}\frac{1}{x + 1} + \frac{2}{x + 2} = \frac{4}{x + 4} \\ \\ \frac{(x + 2) + 2(x + 1)}{(x + 1)(x + 2)} = \frac{4}{x + 4} \\ \\ \frac{x + 2 + 2x + 2}{ {x}^{2} + 3x + 2 } = \frac{4}{x + 4} \\ \\ \frac{3x + 4}{ {x}^{2} + 3x + 2} = \frac{4}{x + 4} \\ \\ (3x + 4)(x + 4) = 4( {x}^{2} + 3x + 2) \\ \\ 3 {x}^{2} + 12x + 4x + 16 = 4 {x}^{2} + 12x + 8 \\ \\ 3 {x}^{2} + 16x + 16 = 4 {x}^{2} + 12x + 8 \\ \\ 3{x}^{2} + 16x + 16 - 4 {x}^{2} - 12x - 8 = 0\\ \\ - {x}^{2} + 4 x + 8= 0 \\ \\ {x}^{2} - 4x - 8 = 0 \\ \\ d \: = {b}^{2} - 4ac \\ \\ d \: = {( - 4)}^{2} - 4 \times 1 \times ( - 8) \\ \\ d = 1 6+ 32 \\ \\ d = 48\\ \\ x \: = \frac{ - b \:± \sqrt{d} }{2a} \\ \\ x = \frac{ 4\:± \sqrt{48} }{2 \times 1 } \\ \\ x \: = \frac{4 \: ± 4 \sqrt{3} }{2} \\ \\ x \: = \frac{2 \: ± 2 \sqrt{3} }{1} \\ \\x = 2 \: ± 2 \sqrt{3} \:$

hope this will help you