Question 148121
*[Tex \LARGE \frac{4}{x^{\frac{2}{3}}}-x^{\frac{1}{3}}] Start with the given expression.



Notice how the LCD is *[Tex \LARGE x^{\frac{2}{3}}]. So we need to multiply the second term *[Tex \LARGE x^{\frac{1}{3}}] by the LCD *[Tex \LARGE x^{\frac{2}{3}}]. 



*[Tex \LARGE \frac{4}{x^{\frac{2}{3}}}-\left(x^{\frac{1}{3}}\right)\left(\frac{x^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)] Multiply the second term by the LCD



*[Tex \LARGE \frac{4}{x^{\frac{2}{3}}}-\left(\frac{x^{\frac{1}{3}}x^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)] Combine the fractions.



*[Tex \LARGE \frac{4}{x^{\frac{2}{3}}}-\left(\frac{x^{\frac{1}{3}+\frac{2}{3}}}{x^{\frac{2}{3}}}\right)] Multiply the terms by adding the exponents.



*[Tex \LARGE \frac{4}{x^{\frac{2}{3}}}-\left(\frac{x^{\frac{3}{3}}}{x^{\frac{2}{3}}}\right)] Add.



*[Tex \LARGE \frac{4}{x^{\frac{2}{3}}}-\left(\frac{x^{1}}{x^{\frac{2}{3}}}\right)] Reduce.



*[Tex \LARGE \frac{4}{x^{\frac{2}{3}}}-\left(\frac{x}{x^{\frac{2}{3}}}\right)] Simplify.



Since the denominators are now the same, we can add the fractions.



*[Tex \LARGE \frac{4-x}{x^{\frac{2}{3}}}] Combine the numerators over the common denominator.



So *[Tex \LARGE \frac{4}{x^{\frac{2}{3}}}-x^{\frac{1}{3}}] simplifies to *[Tex \LARGE \frac{4-x}{x^{\frac{2}{3}}}]


In other words, *[Tex \LARGE \frac{4}{x^{\frac{2}{3}}}-x^{\frac{1}{3}}=\frac{4-x}{x^{\frac{2}{3}}}] where x is positive and {{{x<>0}}}