What is 5/x-(25)/(5x-x^2) ?

The solution to 5/x-(25)/(5x-x^2) is 5/(x-5)

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simplify 5/x-(25)/(5x-x^2)

simplify

\frac{5}{x} - \frac{25}{5 x - x ^{2}}

\frac{5}{x - 5}

Solution steps

\frac{5}{x} - \frac{25}{5 x - x ^{2}}

Least Common Multiplier of

x, 5 x - x^{2} : x (x - 5)

Adjust Fractions based on the LCM

= \frac{5 ( x - 5 )}{x ( x - 5 )} - \frac{- 25}{x ( x - 5 )}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{5 ( x - 5 ) - ( - 25 )}{x ( x - 5 )}

Apply rule:

a - (- b) = a + b

5 (x - 5) - (- 25) = 5 (x - 5) + 25

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

Simplify

5 (x - 5) + 25 : 5 x

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

Cancel the common factor:

x

= \frac{5}{x - 5}

\frac{45}{10}

2 x^{4} + 6 x^{2} - 8

- 812

(3 b - 4) (2 b - 1)

\frac{5}{6} + \frac{\frac{1}{3}}{\frac{6}{7}}