Answer:
see explanation
Step-by-step explanation:
Cross- multiply
Noting that x ≠ [tex]\frac{5}{2}[/tex] as this would make the denominators on both sides zero, that is undefined
(x² - 2)(6x - 15) = (x + 3)(10 - 4x) ← expand parenthesis on both sides
6x³ - 15x² - 12x + 30 = 10x - 4x² + 30 - 12x = - 4x² - 2x + 30
Subtract - 4x² - 2x + 30 from both sides
6x³ - 11x² - 10x = 0 ← in standard form
Factor out x from each term
x(6x² - 11x - 10) = 0
x(3x + 2)(2x - 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x = 0
3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - [tex]\frac{2}{3}[/tex]
2x - 5 = 0 ⇒ 2x = 5 ⇒ x = [tex]\frac{5}{2}[/tex]
Solutions are x = 0, x = - [tex]\frac{2}{3}[/tex]
