What is 4/(x^2-4x)-5/(x^2-2x) ?

The solution to 4/(x^2-4x)-5/(x^2-2x) is (-x+12)/(x(x-4)(x-2))

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simplify 4/(x^2-4x)-5/(x^2-2x)

simplify

\frac{4}{x ^{2} - 4 x} - \frac{5}{x ^{2} - 2 x}

\frac{- x + 12}{x ( x - 4 ) ( x - 2 )}

Solution steps

\frac{4}{x ^{2} - 4 x} - \frac{5}{x ^{2} - 2 x}

Least Common Multiplier of

x^{2} - 4 x, x^{2} - 2 x : x (x - 4) (x - 2)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

4 (x - 2) - 5 (x - 4) : - x + 12

= \frac{- x + 12}{x ( x - 4 ) ( x - 2 )}

- 10 \times 2

- 10 \times 4

(- 4 \frac{1}{2}) 10.4

- 3^{- 8}

\frac{15}{2} + 2

What is 4/(x^2-4x)-5/(x^2-2x) ?
The solution to 4/(x^2-4x)-5/(x^2-2x) is (-x+12)/(x(x-4)(x-2))