Решите дробно-рациональное уравнение 1) 2/x-3=5/x+4 2)3/x+2=8/3-x

Question

Решите дробно-рациональное уравнение
1) 2/x-3=5/x+4
2)3/x+2=8/3-x

Answer 1

1) (2(х+4))/(х-3) = (5(х-3))/(х+4)
(2х+8)/((х-3)(х-4)) - (5х-15)/((х-3)(х+4)) = 0
(2х+8-5х+15)/((х-3)(х+4)) = 0
(-3х+23)/((х-3)(х+4)) = 0
ОДЗ: (х-3)(х+4)≠0; х≠3; х≠ -4
-3х+23 = 0
-3х = -23
х = -23 : (-3)
х = 7 2/3

2) (3(3-х))/((х+2)(3-х)) = (8(х+2))/((х+2)(3-х))
(9-3х)/((х+2)(3-х)) - (8х+16)/((х+2)(3-х)) = 0
(9-3х-8х-16)/((х+2)(3-х)) = 0
(-11х-7)/((х+2)(3-х)) = 0
ОДЗ: (х+2)(3-х)≠0; х≠ -2; х≠3
-11х-7 = 0
-11х = 7
х = 7 : (-11)
х = -7/11

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