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Racionals amb la x al denominador Resol les següents equacions: (MV) a) `(3x-8-9x)/(2x) = 4`
`3x-8-9x = 8x` `3x-9x-8x = 8` `-14x = 8` `x = 8/(-14)` `x = -8/14` `x = -4/7` b) `3/x = 1 + (x-13)/6`
`18/(6x) = (6x)/(6x) + (x^2-13x)/(6x)` `18 = 6x + (x^2-13x)` `18 = 6x + x^2-13x` `18 = x^2-7x` `0 = x^2-7x - 18` `x^2-7x - 18 = 0` `x=(7ħsqrt((-7)^2-4·1·(-18)))/(2·1)` `x=(7ħsqrt(49+72))/2` `x=(7ħsqrt(121))/2` `x=(7ħ11)/2` `x_1=(7+11)/2 = 18/2 = 9` `x_2=(7-11)/2 = -4/2 = -2` c) `1/(x-2)+1/(x+2)=1/(x^2-4)`
`(x+2)/((x-2)·(x+2))+(x-2)/((x-2)·(x+2))=1/((x-2)·(x+2))` `(x+2)+(x-2)=1` `x+2+x-2=1` `2x = 1` `x = 1/2` d) `2/(x^2-x) - 1/(x-1) = 0`
`2/(x·(x-1)) - x/(x·(x-1)) = 0` `2 - x = 0` `- x = -2` `x = 2` e) `1/(x-6) + x/(x-2) = 1/(x^2-8x+12)`
`(x-2)/((x-6)·(x-2)) + (x·(x-6))/((x-6)·(x-2)) = 1/((x-6)·(x-2))` `x-2 + (x·(x-6)) = 1` `x - 2 + x^2-6x = 1` `x^2 - 6x + x - 2 -1 = 0` `x^2 - 5x - 3 = 0` `x=(5ħsqrt(5^2-4·1·(-3)))/(2·1)` `x=(5ħsqrt(25+12))/2` `x=(5ħsqrt(37))/2` `x_1=(5+sqrt(37))/2` `x_2=(5-sqrt(37))/2` |