Question

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Answer 1

Step-by-step explanation:

1/x+1+1/x+2=2/x+10

x+2+x+1/x^2+3x+2=2/x+10

(2x+3)(x+10)=2[(x+1)(x+2)]

2x^2+20x+3x+30=2(x^2+3x+2)

2x^2+23x+30=2x^2+6x+4

23x-6x+30-4=0

17x+26=0

17x=-26

x=-26/17. Answer

Answer 2

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

__________ [ GIVEN ]

• We have to find the value of x.

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

→ $\frac{x \: + \: 2 \: + \: x \: + \: 1}{(x\:+\:1)(x \: + \: 2)}\:=\:\frac{2}{x\:+\:10}$

→ $\frac{2x \: + \: 3}{x(x \: + \: 2) \: + 1(x \: + \: 2)}\:=\:\frac{2}{x\:+\:10}$

→ $\frac{2x \: + \: 3}{ {x}^{2} \: + \: 2x \: + \: x \: + \: 2}\:=\:\frac{2}{x\:+\:10}$

→ $\frac{2x \: + \: 3}{ {x}^{2} \: + \: 3x \: + \: 2}\:=\:\frac{2}{x\:+\:10}$

Cross-multiply them

→ $(x \: + \: 10)(2x \: + \: 3) \: = \: 2( {x}^{2} \: + \: 3x \: + \: 2)$

→ $x(2x \: + \: 3) \: + 10(2x \: + \: 3)\: = \: 2{x}^{2} \: + \: 6x \: + \: 4$

→ $2 {x}^{2} \: + \: 3x \: + \:20x \: + \: 30\: = \: 2{x}^{2} \: + \: 6x \: + \: 4$

→ $2 {x}^{2} \: + \: 23x \: + \: 30\: = \: 2{x}^{2} \: + \: 6x \: + \: 4$

→ $2 {x}^{2} \: - \: 2 {x}^{2} + \: 23x \: - \: 6x \: + \: 30\: - \: 4 \: = \: 0$

→ $17x\: + \: 26\: = \: 0$

→ $17x\: = \:-\: 26$

→ $x\:=\:-\:26/17$

→ $x\:=\:-\:1.529$

→ $x\:=\:-\:1.5$ (approx.)

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x = - 1.5

________ [ ANSWER ]

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