Đáp án:
a, `x/(x - 1) = (x + 4)/(x + 1)` `(ĐKXĐ : x ne ±1)`
`<=> x(x + 1) = (x + 4)(x - 1)`
`<=> x^2 + x = x^2 + 4x - x - 4`
`<=> x^2 + x - x^2 - 3x + 4 = 0`
`<=> -2x + 4 = 0`
`<=> -2x = -4`
`<=> x = 2`
b, `(x + 2)/x = (2x + 3)/[2(x - 2)]` `(ĐKXĐ : x ne 0, 2)`
`<=> (x + 2).2(x - 2) = (2x + 3)x`
`<=> 2(x^2 - 4) = 2x^2 + 3x`
`<=> 2x^2 - 8 = 2x^2 + 3x`
`<=> -8 = 3x`
`<=> x = -8/3`
c, `x/[2(x - 3)] + x/(2x + 2) = (2x)/[(x + 1)(x - 3)]` `(ĐKXĐ : x ne 3, -1)`
`<=> x/[2(x - 3)] + x/[2(x + 1)] = (2x)/[(x + 1)(x - 3)]`
`<=> [x(x + 1)]/[2(x - 3)(x + 1)] + [x(x - 3)]/[2(x + 1)(x - 3)] = (2.2x)/[2(x + 1)(x - 3)]`
`<=> (x^2 + x)/[2(x - 3)(x + 1)] + (x^2 - 3x)/[2(x - 3)(x + 1)] = (4x)/[2(x - 3)(x + 1)] `
`<=> (x^2 + x + x^2 - 3x)/[2(x - 3)(x + 1)] = (4x)/[2(x - 3)(x + 1)]`
`<=> (2x^2 - 2x)/[2(x - 3)(x + 1)] = (4x)/[2(x - 3)(x + 1)] `
`<=> 2x^2 - 2x = 4x`
`<=> 2x^2 - 2x - 4x = 0`
`<=> 2x^2 - 6x = 0`
`<=> 2x(x - 3) = 0`
<=> \(\left[ \begin{array}{l}x=0\\x - 3 = 0\end{array} \right.\)
<=> \(\left[ \begin{array}{l}x=0\\x=3\end{array} \right.\)
Kết hợp ĐKXĐ
`=> x = 0`
d, `(2x - 5)/(x + 5) = 3` `(ĐKXĐ : x ne -5)`
`<=> 2x - 5 = 3(x + 5)`
`<=> 2x - 5 = 3x + 15`
`<=> 3x + 15 - 2x + 5 = 0`
`<=> x + 20 = 0`
`<=> x = -20`
e, `(x^2 - 6)/x = x + 3/2` `(ĐKXĐ : x ne 0)`
`<=> x^2/x - 6/x = x + 3/2`
`<=> x - 6/x = x + 3/2`
`<=> -6/x = 3/2`
`<=> (-6).2 = 3.x`
`<=> -12 = 3x`
`<=> x = -4`
Giải thích các bước giải:
