How do you solve $(2 + \frac{5}{x}) = (\frac{3}{x^{2}})$ $(2 + 5/x) = (3/x^2)$ ?

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Answer 1 · 2018-04-06T11:33:28

$x = \frac{1}{2} or x = - 3$ $x=1/2 or x=-3$

$2 + \frac{5}{x} = \frac{3}{x^{2}}$ $2+5/x=3/x^2$

$2 x^{2} + 5 x = 3$ $2x^2+5x=3$ multiply both sides by $x^{2}$ $x^2$

$2 x^{2} + 5 x - 3 = 0$ $2x^2+5x-3=0$ subtract $3$ $3$ from both sides

$(2 x - 1) (x + 3) = 0$ $(2x-1)(x+3)=0$ factorise trinomial

$2 x - 1 = 0 or x + 3 = 0$ $2x-1=0 or x+3=0$ solve quadratic equation

$x = \frac{1}{2} or x = - 3, (x \neq 0)$ $x=1/2 or x=-3 ,(x!=0)$

How do you solve (2 + 5/x) = (3/x^2)(2+5x)=(3x2)(2 + 5/x) = (3/x^2)?