Đáp án:
Bài `1`
`a)`
` => -3/(1-5x) -2/(5x-3) = 4/((1-5x)(5x-3))`
` => -3.(5x-3) - 2(1-5x) = 4`
` => -15x + 9 - 2 + 10x =4`
` => -5x + 7 = 4`
` => -5x = -3`
` => x =3/5`
`b)`
` => (5-x)/(4x(x-2)) + 7/8 = (x-1)/(2x(x-2)) + 1/(8(x-2x))`
` = (2(5-x)/(8x(x-2)) + (7x(x-2))/(8x(x-2)) = (4(x-1))/(8x(x-2)) + x/(8(x-2x))`
` => 2(5-x) + 7x(x-2) = 4(x-1) + x`
` => 10 - 2x + 7x^2 - 14x - 4x + 4 - x = 0`
` => 7x^2 - 21x + 14 = 0`
` => x^2 -3x + 2 = 0`
` => (x-1)(x-2)= 0`
` => `\(\left[ \begin{array}{l}x=1\\x=2\end{array} \right.\)
`c)`
`=> ((x^2 -x)(x-3))/(x^2 -9) - (x^2(x+3))/(x^2-9) = (-7x^2 +3x)/(x^2-9)`
` => (x^2-x)(x-3) - x^2(x+3) = -7x^2 + 3x`
` => x^3 -3x^2 - x^2 + 3x - x^3 - 3x^2 + 7x^2 - 3x = 0`
` => -3x = 0`
` => x = 0`
`d)`
` => ((x+6)^2)/(x^2+x-30) + ((x-5)^2)/(x^2+x-30) = (2x^2+23x+61)/(x^2+x-30)`
` => (x+6)^2 + (x-5)^2 = 2x^2 +23x + 61`
` => x^2 + 12x + 36 + x^2 - 10x + 25 - 2x^2 - 23x - 61 = 0`
`=> -21x = 0`
` => x =0`
`e)`
` => (8+x^3)/(8+x^3) + (x^2-2x+4)/(8+x^3) = 12/(8+x^3)`
` => 8+x^3 + x^2 - 2x +4 = 12`
` => x^3 + x^2 - 2x +12 = 12`
` => x^3 +x^2 -2x = 0`
` => x(x^2 + x -2) = 0`
` => x(x-1)(x+2) = 0`
` => x =0 ; x =1; x =-2`
