Nyatakan ke bentuk paling sederhana dalam pangkat positif a. x/y^(-1) + y/x^(-2) b. xpangkat-1

September 2018 1 38 Report

Nyatakan ke bentuk paling sederhana dalam pangkat positif

a. x/y^(-1) + y/x^(-2)
b. xpangkat-1 - y^3 di/semua x^-5 + y^-2

Takamori37 Jika terjadi kesalahan interpretasi jawaban, harap beritahu.
Dalam pangkat positif,

Bagian a.
$$\begin{align}\frac{x}{y^{-1}}+\frac{y}{x^{-2}}&=xy^{-(-1)}+x^{-(-2)}y \\ &=xy+x^2y \\ &=xy(1+x)\end{align}$

Bagian b.
$$\begin{align}\frac{x^{-1}-y^3}{x^{-5}+y^{-2}}&=\frac{\frac{1}{x}+y^3}{\frac{1}{x^5}+\frac{1}{y^2}} \\ &=\frac{\frac{1+y^3}{x}}{\frac{y^2+x^5}{x^5y^2}}=\frac{1+y^3}{x}:\frac{x^5+y^2}{x^5y^2} \\ &=\frac{1+y^3}{x}\times\frac{x^5y^2}{x^5+y^2} \\ &=\frac{x^5y^2(1+y^3)}{x(x^5+y^2)} \\ &=\frac{x^4y^2(1+y^3)}{x^5+y^2}\end{align}$

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