Question

What are the x intercepts for 5/x + 1/3x = 4x/3

Answer 1

`\bf \cfrac{5}{x}+\cfrac{1}{3}x=\cfrac{4x}{3}\implies \cfrac{5}{x}+\cfrac{x}{3}=\cfrac{4x}{3}`

now, the cheap answer will be, let's just get the LCD of all those fractions, hmm let's see is 3x, and multiply all the fractions by the LCD, that way, getting rid of the denominators.


`\bf \cfrac{5}{x}+\cfrac{1}{3}x=\cfrac{4x}{3}\implies \cfrac{5}{x}+\cfrac{x}{3}=\cfrac{4x}{3}\impliedby * \stackrel{LCD}{3x} \\\\\\ \boxed{3x}\cdot \cfrac{5}{x}+\boxed{3x}\cdot \cfrac{x}{3}=\boxed{3x}\cdot \cfrac{4x}{3}\implies 15+x^2=4x^2\implies 15=3x^2 \\\\\\ \cfrac{15}{3}=x^2\implies 5=x^2\implies \pm√(5)=x`