Question

find the roots of 1/x+4-1/x-7=11/30
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Answer 1

Step-by-step explanation:

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

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

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

(x+4)(x-7) = -30

x^2-3x-28 = -30

x^2-3x = -2

x^2-3x+2 = 0

x^2-2x-x+2 = 0

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

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

x=1 or 2

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Answer 2

Answer:

x = 1 , 2

Step-by-step explanation:

Given

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

By doing the cross multiplication, we get,

=> 30 = 11(x²-3x-28)/(-11)

=> 30 = -(x²-3x-28)

=> x²-3x-28+30 =0

=> x²-3x+2=0

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

=> x = 1,2

Therefore,

Roots of the given quadratic equation are 1 , 2