What is ((x+4)/5-1/x)/(1-\frac{25){x^2}} ?

The solution to ((x+4)/5-1/x)/(1-\frac{25){x^2}} is ((x-1)x)/(5(x-5))

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simplify ((x+4)/5-1/x)/(1-\frac{25){x^2}}

simplify

\frac{\frac{x + 4}{5} - \frac{1}{x}}{1 - \frac{25}{x ^{2}}}

\frac{( x - 1 ) x}{5 ( x - 5 )}

Solution steps

\frac{\frac{x + 4}{5} - \frac{1}{x}}{1 - \frac{25}{x ^{2}}}

Join

\frac{x + 4}{5} - \frac{1}{x} : \frac{x ^{2} + 4 x - 5}{5 x}

= \frac{\frac{x ^{2} + 4 x - 5}{5 x}}{1 - \frac{25}{x ^{2}}}

Join

1 - \frac{25}{x ^{2}} : \frac{x ^{2} - 25}{x ^{2}}

= \frac{\frac{x ^{2} + 4 x - 5}{5 x}}{\frac{x ^{2} - 25}{x ^{2}}}

Apply the fraction rule:

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

= \frac{( x ^{2} + 4 x - 5 ) x ^{2}}{5 x ( x ^{2} - 25 )}

Cancel

\frac{( x ^{2} + 4 x - 5 ) x ^{2}}{5 x ( x ^{2} - 25 )} : \frac{( x - 1 ) x}{5 ( x - 5 )}

= \frac{( x - 1 ) x}{5 ( x - 5 )}

5 (2 x^{2} y^{3} z)

\frac{x ^{2} + 3 x + 2}{x ^{2} - 2 x + 1} - \frac{3 x + 3}{x ^{2} - 2 x + 1}

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What is ((x+4)/5-1/x)/(1-\frac{25){x^2}} ?
The solution to ((x+4)/5-1/x)/(1-\frac{25){x^2}} is ((x-1)x)/(5(x-5))