Question

x-4/x-5+x-6/x-7=10/3

Answer 1

⇒ (x-4) / (x-5) + (x-6) / (x-7) = 10/3
⇒ (x-4) (x-7)  + (x-5) (x-6) = 10 [ (x-5) (x-7) ]
⇒ 3 [x2 -11x +28 + x2 -11x + 30] = 10 [ x2 -12x + 35 ]
⇒ 3 [ 2x2- 22x + 58 ] = 10x2 -120x + 350
⇒ 4x2- 54x + 176 = 0
⇒ 2x2- 27x + 88 = 0
a = 2, b = -27,c = 88
x =  [ 27±√(729 - 704) ] / 4
x =  [ 27± 5] / 4
x values are 8, 11/2

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Answer 2

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