What is 5/(x-1)-x/(x-8) ?

The solution to 5/(x-1)-x/(x-8) is (-x^2+6x-40)/((x-1)(x-8))

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simplify 5/(x-1)-x/(x-8)

simplify

\frac{5}{x - 1} - \frac{x}{x - 8}

\frac{- x ^{2} + 6 x - 40}{( x - 1 ) ( x - 8 )}

Solution steps

\frac{5}{x - 1} - \frac{x}{x - 8}

Least Common Multiplier of

x - 1, x - 8 : (x - 1) (x - 8)

Adjust Fractions based on the LCM

= \frac{5 ( x - 8 )}{( x - 1 ) ( x - 8 )} - \frac{x ( x - 1 )}{( x - 1 ) ( x - 8 )}

Apply the fraction rule:

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

= \frac{5 ( x - 8 ) - x ( x - 1 )}{( x - 1 ) ( x - 8 )}

Simplify

5 (x - 8) - x (x - 1) : - x^{2} + 6 x - 40

= \frac{- x ^{2} + 6 x - 40}{( x - 1 ) ( x - 8 )}

(- 5 - i) (2 + 4 i)

ln (1.05)

(x - 4) (x^{2} + 4 x + 16)

\frac{4 x}{x ^{2}}

What is 5/(x-1)-x/(x-8) ?
The solution to 5/(x-1)-x/(x-8) is (-x^2+6x-40)/((x-1)(x-8))