Question

SOLVE FOR x
1/(x+1)+1/(x+2)=2/(x+10)
SOLVE IN THE EASIEST WAY.....​

Answer 1

Answer:

x= - 1 integer 9/17

Step-by-step explanation:

solution is attached may be helpful

Answer 2

Question:

$\frac{1}{x + 1} + \frac{1}{x + 2} = \frac{2}{x + 10}$

Answer:

Taking LCM by cross multiplying denominators.

$\implies\frac{1}{x + 1} + \frac{1}{x + 2} = \frac{2}{x + 10} \\ \\ \implies \: \frac{1(x + 2) + 1(x + 1)}{(x + 1)(x + 2)} = \frac{2}{x + 10} \\ \\ \implies \: \frac{x + 2 + x + 1}{x(x + 2) + 1(x + 2)} = \frac{2}{x + 10} \\ \\ \implies \: \frac{2x + 3}{ {x}^{2} + 2x + x + 2} = \frac{2}{x + 10} \\ \\ \implies \: \frac{2x + 3}{ {x}^{2} + 3x + 2} = \frac{2}{x + 10} \\ \\ Again\: cross\: multiplying \\ \\ \implies \: {(2x + 3)(x + 10)} = 2( {x}^{2} + 3x + 2) \\ \\ \small\implies \: 2x(x + 10) + 3(x + 10) = 2 {x}^{2} + 6x + 4 \\ \\ \small \implies \: 2 {x}^{2} + 20x + 3 x + 30 = 2 {x}^{2} + 6x + 4 \\ \\ \implies \: 2 {x}^{2} + 23x + 30 = 2 {x}^{2} + 6x + 4 \\ \\ \implies \: \cancel{2 {x}^{2} } + 23x + 30 = \cancel{2 {x}^{2} } + 6x + 4 \\ \\ \implies \: 23x - 6x = 4 - 30 \\ \\ \implies \: 17x = - 26 \\ \\ \implies \: x = - \frac{26}{17}$

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