Question

Rezolvati in R

Dau Coroana​

Answer 1

Explicație pas cu pas:

$\frac{2x+3}{x-2} - \frac{8x-2}{x(x-2)} = \frac{3x+1}{x}$

Aducem la acelasi numitor =>

x(2x+3) - (8x-2) = (x-2)(3x+1)

$2x^2 + 3x - 8x + 2 = 3x^2 - 6x + x - 2$

$x^2 = 4$

x = {-2, 2}

Answer 2

( 2x + 3 )/( x - 2 ) - ( 8x - 2 )/( x² - 2x ) = ( 3x + 1 )/x

( 2x + 3 )/( x - 2 ) - ( 8x - 2 )/[ x ( x - 2 )] = ( 3x + 1 )/x

x ( 2x + 3 ) - ( 8x - 2 ) = ( x - 2 )( 3x + 1 )

2x² + 3x - 8x + 2 = 3x² + x - 6x - 2

2x² - 5x + 2 - 3x² + 5x +  2 = 0

-x² + 4 = 0

-x² = -4  | · (-1)

x² = 4 ⇒ x₁ = -2 ; x₂ = 2

S = { -2 ; 2 }