Question

solve: 1/x+2+1/x=3/4​

Answer 1

EXPLANATION.

⇒ 1/(x + 2) + 1/(x) = 3/4.

As we know that,

⇒ x + x + 2/(x + 2)(x) = 3/4.

⇒ 2x + 2/(x + 2)(x) = 3/4.

⇒ 4(2x + 2) = 3(x + 2)(x).

⇒ 8x + 8 = 3(x² + 2x).

⇒ 8x + 8 = 3x² + 6x.

⇒ 3x² + 6x - 8x - 8 = 0.

⇒ 3x² - 2x - 8 = 0.

Factorizes the equation into middle term splits, we get.

⇒ 3x² - 6x + 4x - 8 = 0.

⇒ 3x(x - 2) + 4(x - 2) = 0.

⇒ (3x + 4)(x - 2) = 0.

⇒ x = -4/3  and  x = 2.

Answer 2

Step-by-step explanation:

$\tt \frac{1}{x} + 2 + \frac{1}{x} = \frac{3}{4} \\ --------------------------- \\ \tt \: LCM \: ofx \: and \: 4 = 4x \\--------------------------- \\ \longrightarrow \: \tt \frac{1}{x} + 2 + \frac{1}{x} = \tt \frac{3}{4} \\\ \tt \: \longrightarrow ( \frac{1}{ \cancel{x}} \times 4 \cancel{x}) +( 2 \times 4x) + (\frac{1}{ \cancel{x}} \times 4 \cancel{x } )= (\frac{3}{ \cancel{4}} \times \cancel{4}x) \\ \longrightarrow \tt \: 4 + 8x + 4 = 3x \\ \longrightarrow \tt \: 5x = - 8 \\ \longrightarrow \tt \: x = |\red{ \frac { - 8}{5} }| \\ ---------------------------$