Jika y-x= -1, maka bentuk: { (x^½)-(y^½) } / { (x^½)+(y^½) } dapat diubah menjadi .... Question from @michele118

October 2018 1 13 Report

Jika y-x= -1, maka bentuk:
{ (x^½)-(y^½) } / { (x^½)+(y^½) } dapat diubah menjadi ...

izharulhaq78 $\displaystyle \frac{x^{\frac12}-y^{\frac12}}{x^{\frac12}+y^{\frac12}}=\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\\\text{rasionalkan}\\\frac{x^{\frac12}-y^{\frac12}}{x^{\frac12}+y^{\frac12}}=\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\times\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\\\frac{x^{\frac12}-y^{\frac12}}{x^{\frac12}+y^{\frac12}}=\frac{(\sqrt{x}-\sqrt{y})^2}{(\sqrt{x})^2-(\sqrt{y})^2}\\\frac{x^{\frac12}-y^{\frac12}}{x^{\frac12}+y^{\frac12}}=\frac{x-2\sqrt{xy}+y}{x-y}$
$\displaystyle \frac{x^{\frac12}-y^{\frac12}}{x^{\frac12}+y^{\frac12}}=\frac{x-2\sqrt{xy}+y}{-(y-x)}\\\frac{x^{\frac12}-y^{\frac12}}{x^{\frac12}+y^{\frac12}}=\frac{x+y-2\sqrt{xy}}{-(-1)}\\\frac{x^{\frac12}-y^{\frac12}}{x^{\frac12}+y^{\frac12}}=\frac{x+y-2\sqrt{xy}}{1}\\\boxed{\boxed{\frac{x^{\frac12}-y^{\frac12}}{x^{\frac12}+y^{\frac12}}=x+y-2\sqrt{xy}}}$

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{ ((x^2/3)+(x^1/2))*((x^1/3)-(1/(x^1/3))) } / { ((x^1/2)+1/(x^1/2))*(x-(x^1/3)) } =...