What is (x/y+1)/(x/y-1) ?

The solution to (x/y+1)/(x/y-1) is (y+x)/(-y+x)

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simplify (x/y+1)/(x/y-1)

simplify

\frac{\frac{x}{y} + 1}{\frac{x}{y} - 1}

\frac{y + x}{- y + x}

Solution steps

\frac{\frac{x}{y} + 1}{\frac{x}{y} - 1}

Join

\frac{x}{y} + 1 : \frac{y + x}{y}

= \frac{\frac{y + x}{y}}{\frac{x}{y} - 1}

Join

\frac{x}{y} - 1 : \frac{- y + x}{y}

= \frac{\frac{y + x}{y}}{\frac{- y + x}{y}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( y + x ) y}{y ( - y + x )}

Cancel the common factor:

y

= \frac{y + x}{- y + x}

7 x = 4 x + 30

(1 + 3 i) (1 - 3 i)

36 x^{6} y^{5} - 21 x^{8} y^{4} + 6 x^{5} y^{2}

261

4 x^{2} - x + 1 = 0