Rozwiąż równanie : a) x-3/x-5 = 2+5-x/x-7 b) (3x-5/x+1) = 4
a) x-3/x-5 = 2+5-x/x-7
(x-3)(x-7)=(x-5)(2+5-x)
x^{2} -7x-3x+21=2x+5x-x^{2}-10-25+5x
x^{2}-10x+21=-x^{2}+12x-35
2x^{2}-22x+56=0
delta=484-448=36x1=22+6/4=7x2=22-6/4=4
b) (3x-5/x+1) = 4
4(x+1)=3x-5
4x+1=3x-5
x=-6
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a) x-3/x-5 = 2+5-x/x-7
(x-3)(x-7)=(x-5)(2+5-x)
x^{2} -7x-3x+21=2x+5x-x^{2}-10-25+5x
x^{2}-10x+21=-x^{2}+12x-35
2x^{2}-22x+56=0
delta=484-448=36
x1=22+6/4=7
x2=22-6/4=4
b) (3x-5/x+1) = 4
4(x+1)=3x-5
4x+1=3x-5
x=-6