Question

find the root of the equation 1/x+4-1/x-7=11/30,x≠-4,7​

Answer 1

The values are   x = 1 or x = 2

Step-by-step explanation:

Given data:

1/x+4 - 1/x-7 = 11/30

[(x - 7 - (x+4)] / (x +4) (x -7) = 11/30

(x - 7 - x - 4)/ x^2 - 7x +4x - 28 = 11/30

-11/ x^2 -3x - 28 = 11/30

Do the cross multiplication, we get

 30 = 11(x²-3x-28)/(-11)

 30 = -(x²-3x-28)

x²-3x-28+30 =0

x²-3x+2=0

Now splitting the middle term, we get

 x²-1x-2x+2 =0

x(x-1)-2(x-1)=0

 (x-1)(x-2)=0

x-1 = 0 or x-2 = 0

 x = 1 or x = 2

Thus the values are   x = 1 or x = 2

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