What is (5/(3r-1)-5)/(5/(3r-1)+5) ?

The solution to (5/(3r-1)-5)/(5/(3r-1)+5) is (-3r+2)/(3r)

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simplify (5/(3r-1)-5)/(5/(3r-1)+5)

simplify

\frac{\frac{5}{3 r - 1} - 5}{\frac{5}{3 r - 1} + 5}

\frac{- 3 r + 2}{3 r}

Solution steps

\frac{\frac{5}{3 r - 1} - 5}{\frac{5}{3 r - 1} + 5}

Join

\frac{5}{3 r - 1} - 5 : \frac{- 15 r + 10}{3 r - 1}

= \frac{\frac{- 15 r + 10}{3 r - 1}}{\frac{5}{3 r - 1} + 5}

Join

\frac{5}{3 r - 1} + 5 : \frac{15 r}{3 r - 1}

= \frac{\frac{- 15 r + 10}{3 r - 1}}{\frac{15 r}{3 r - 1}}

Apply the fraction rule:

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

= \frac{( - 15 r + 10 ) ( 3 r - 1 )}{( 3 r - 1 ) \cdot 15 r}

Cancel

\frac{( - 15 r + 10 ) ( 3 r - 1 )}{( 3 r - 1 ) \cdot 15 r} : \frac{- 3 r + 2}{3 r}

= \frac{- 3 r + 2}{3 r}

\frac{35}{45}

4 x^{- 4} \cdot \frac{1}{2} x^{2}

(x + 1) (x - 3)^{2}

a (2 + x) - (2 + x)

(- 10 + 8 i) - (- 4 - 4 i)

What is (5/(3r-1)-5)/(5/(3r-1)+5) ?
The solution to (5/(3r-1)-5)/(5/(3r-1)+5) is (-3r+2)/(3r)