What is x/(x-6)-(x-3)/(3x) ?

The solution to x/(x-6)-(x-3)/(3x) is (2x^2+9x-18)/(3x(x-6))

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simplify x/(x-6)-(x-3)/(3x)

simplify

\frac{x}{x - 6} - \frac{x - 3}{3 x}

\frac{2 x ^{2} + 9 x - 18}{3 x ( x - 6 )}

Solution steps

\frac{x}{x - 6} - \frac{x - 3}{3 x}

Least Common Multiplier of

x - 6, 3 x : 3 x (x - 6)

Adjust Fractions based on the LCM

= \frac{3 x ^{2}}{3 x ( x - 6 )} - \frac{( x - 3 ) ( x - 6 )}{3 x ( x - 6 )}

Apply the fraction rule:

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

= \frac{3 x ^{2} - ( x - 3 ) ( x - 6 )}{3 x ( x - 6 )}

Simplify

3 x^{2} - (x - 3) (x - 6) : 2 x^{2} + 9 x - 18

= \frac{2 x ^{2} + 9 x - 18}{3 x ( x - 6 )}

(x - 1) (y - 1)

x^{3} + 13 x^{2} + 40 x + 36

43 \cdot 26

\frac{0}{13}

\frac{1}{4 + 2 i}

What is x/(x-6)-(x-3)/(3x) ?
The solution to x/(x-6)-(x-3)/(3x) is (2x^2+9x-18)/(3x(x-6))