What is x/(5x-6)-(x+3)/(6x) ?

The solution to x/(5x-6)-(x+3)/(6x) is (x^2-9x+18)/(6x(5x-6))

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simplify x/(5x-6)-(x+3)/(6x)

simplify

\frac{x}{5 x - 6} - \frac{x + 3}{6 x}

\frac{x ^{2} - 9 x + 18}{6 x ( 5 x - 6 )}

Solution steps

\frac{x}{5 x - 6} - \frac{x + 3}{6 x}

Least Common Multiplier of

5 x - 6, 6 x : 6 x (5 x - 6)

Adjust Fractions based on the LCM

= \frac{6 x ^{2}}{6 x ( 5 x - 6 )} - \frac{( x + 3 ) ( 5 x - 6 )}{6 x ( 5 x - 6 )}

Apply the fraction rule:

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

= \frac{6 x ^{2} - ( x + 3 ) ( 5 x - 6 )}{6 x ( 5 x - 6 )}

Simplify

6 x^{2} - (x + 3) (5 x - 6) : x^{2} - 9 x + 18

= \frac{x ^{2} - 9 x + 18}{6 x ( 5 x - 6 )}

2 + 1

lo g_{3} (36)

(x + 1) (2 x^{2} - 3 x - 7)

4 + 4

9 \cdot 8 \cdot 7 \cdot 6

What is x/(5x-6)-(x+3)/(6x) ?
The solution to x/(5x-6)-(x+3)/(6x) is (x^2-9x+18)/(6x(5x-6))