Question

`1 +1/x=12/x^(2)`

Answer 1

x = -4 , 3

Explanation:

To find the value of x, simplify the equation and write in the quadratic equation in the standard form: ax² + bx + c = 0

`\sf 1 + (1)/(x)= (12)/(x^2)`

Multiply the entire equation by x²,

`\sf x^2 * 1 + x^2 *(1)/(x)= x^2 *(12)/(x^2)\\\\\\x^2 + x = 12\\\\x^2 + x - 12 = 0`

Factorize the equation to find the value of x.

Sum = 1

Product = -12

Factors = 4 , (-3)

When we multiply the factors 4 *(-3), we get (-12).

When we combine the factors 4 + (-3), we get 1.

Rewrite the middle term using the factors.

x² + 4x - 3x - 12 = 0

x( x + 4) - 3(x + 4) = 0

(x +4)(x - 3) = 0

x + 4 = 0 ; x - 3 = 0

x = -4 ; x = 3

Answer: x = -4, 3