Question

determine the solution.
$\frac{5x + 20}{x^{2}}=\frac{4}{x}$

Explanation:

Step1: Cross - multiply

$(5x + 20)x=4x^{2}$

Step2: Expand left - hand side

$5x^{2}+20x = 4x^{2}$

Step3: Move all terms to one side

$5x^{2}-4x^{2}+20x=0$
$x^{2}+20x = 0$

Step4: Factor out x

$x(x + 20)=0$

Step5: Solve for x

$x=0$ or $x=-20$
But when $x = 0$, the original equation $\frac{5x + 20}{x^{2}}=\frac{4}{x}$ has undefined terms (division by zero). So we discard $x = 0$.

Answer:

$x=-20$