Question

Hey guys I needed a help Solve 2x -3/x=1

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

2x - $\frac{3}{x}$ = 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 = $\frac{3}{2}$