Question

find the roots of the following equation 1/x+4-1/x-7= -4/7
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Answer 1

Step-by-step explanation:

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

take LCM of x and x-7

therefore,

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

x-7 + 4x-x / x^2 - 7x = -4/7

4x-7 / x^2 - 7x = -4/7

By cross multiplication method

28x- 7. = 4x^2 + 28x

Here 28x and 28x canclled out.

therefore,

- 4x^2 - 7 = 0

-(2x)^2 - (root 7)^2 =0

(-2x+ root 7)(-2x - root 7) =0

Now,

# -2x + root 7 = 0

x = - root 7 /-2 = root 7/2

# -2x - root 7 = 0

x = root 7/ - 2

= -root 7/ 2

# -2x - root 7 = -