Answer:
Explanation:
x=±\dfrac{2}{\sqrt{3}}
Step-by-step explanation:
We want to solve the equation
\dfrac{3x}{4}=\dfrac{1}{x}
We first have to assume that x\\eq 0 since the value \dfrac{1}{x} is not defined for x\\eq 0.
Now, since x divides the right hand side of the equation, we multiply the two sides of this equation by x to get that
x(\frac{3}{4}x)=x(\dfrac{1}{x})\quad\Rightarrow\quad \dfrac{3}{4}x^2=1
Hence, by dividing the equation by \dfrac{4}{3} it follows that
x^2=\dfrac{4}{3}
and so
x=\pm\dfrac{2}{\sqrt{3}}