Question

Answer 1

\(\dfrac{90\left(x-6\right)}{x\left(x-6\right)}-\dfrac{36x}{x\left(x-6\right)}=\dfrac{2x\left(x-6\right)}{x\left(x-6\right)}\)

\(\Leftrightarrow90x-540-36x=2x^2-12x\)

\(\Leftrightarrow-2x^2+90x-36x+12x-540=0\)

\(\Leftrightarrow-2x^2+66x-540=0\)

\(\Leftrightarrow x^2-33x+270=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=18\\x=15\end{matrix}\right.\)

 

Answer 2

`90 / x - 36 / [ x - 6 ] = 2`         `ĐK: x \ne 0,x \ne 6`

`<=> [ 90 ( x - 6 ) - 36x ] / [ x ( x - 6 ) ] = [ 2x ( x - 6 ) ] / [ x ( x - 6 ) ]`

   `=> 90x - 540 - 36x = 2x^2 - 12x`

`<=> 2x^2 - 66x + 540 = 0`

`<=> 2x^2 - 30x - 36x + 540 = 0`

`<=> 2x ( x - 15 ) - 36 ( x - 15 ) = 0`

`<=> ( x - 15 ) ( 2x - 36 ) = 0`

`<=>` $\left[\begin{matrix} x - 15 = 0\\ 2x-36=0\end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=15\\ x=18\end{matrix}\right.$    (t/m)

Vậy `S = { 15 ; 18 }`

 

Answer 3

90 : x - 36 : (x-6) = 2

90 : x - 36 : x - 36 : 6 = 2

90 : x - 36 : x - 6        = 2

90 : x - 36 : x             = 2 + 6

90 : x - 36 : x             = 8

(90 - 36) : x               = 8

54 : x = 8

x = 54 : 8

x = 6,75

Answer 4

i, 90/x - 36/x - 6 = 2       ( ĐKXĐ: x ≠ 0;6)

=> 90(x - 6) - 36x = 2x(x - 6)

<=> 90x - 540 - 36x = 2x² - 12x

<=> 90x - 36x - 2x² + 12x = 540

<=> 66x - 2x² = 540

<=> -2x² + 66x - 540 = 0

<=> (x - 18)(-2x + 30) = 0

*TH1: x - 18 = 0 <=> x = 18 (Tm)

*TH2: -2x + 30 = 0 <=> x = 15  (Tm)

Vậy tập nghiệm pt S = { 15; 18 }