What is (5/x-3)/(5/x+3) ?

The solution to (5/x-3)/(5/x+3) is (-3x+5)/(3x+5)

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simplify (5/x-3)/(5/x+3)

simplify

\frac{\frac{5}{x} - 3}{\frac{5}{x} + 3}

\frac{- 3 x + 5}{3 x + 5}

Solution steps

\frac{\frac{5}{x} - 3}{\frac{5}{x} + 3}

Join

\frac{5}{x} - 3 : \frac{- 3 x + 5}{x}

= \frac{\frac{- 3 x + 5}{x}}{\frac{5}{x} + 3}

Join

\frac{5}{x} + 3 : \frac{3 x + 5}{x}

= \frac{\frac{- 3 x + 5}{x}}{\frac{3 x + 5}{x}}

Apply the fraction rule:

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

= \frac{( - 3 x + 5 ) x}{x ( 3 x + 5 )}

Cancel the common factor:

x

= \frac{- 3 x + 5}{3 x + 5}

\frac{5}{6} \times 8

n^{2} + n - 90

4 \times 45

\frac{( x + 1 )}{x}

- \frac{8}{3} - 1