Question

8. Find the roots of the equation
1/x+4-1/ x-7 =1/30x≠-4,+7.​

Answer 1

Answer:

1 Or 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 -3x -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

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

Therefore,

Roots of the given quadratic equation are 1 , 2