Answer:
see explanation
Step-by-step explanation:
Given
2x - [tex]\frac{3}{x}[/tex] = 1
Multiply through by x
2x² - 3 = x ( subtract x from both sides )
2x² - x - 3 = 0 ← in standard form
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
The factors are + 2 and - 3
product = 2 × - 3 = - 6 and sum = 2 - 3 = - 1
Use these factors to split the x- term
2x² + 2x - 3x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(x + 1) - 3(x + 1) = 0 ← factor out (x + 1) from each term
(x + 1)(2x - 3) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
