What is x/(5x-6)-(x-1)/(7x) ?

The solution to x/(5x-6)-(x-1)/(7x) is (2x^2+11x-6)/(7x(5x-6))

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simplify x/(5x-6)-(x-1)/(7x)

simplify

\frac{x}{5 x - 6} - \frac{x - 1}{7 x}

\frac{2 x ^{2} + 11 x - 6}{7 x ( 5 x - 6 )}

Solution steps

\frac{x}{5 x - 6} - \frac{x - 1}{7 x}

Least Common Multiplier of

5 x - 6, 7 x : 7 x (5 x - 6)

Adjust Fractions based on the LCM

= \frac{7 x ^{2}}{7 x ( 5 x - 6 )} - \frac{( x - 1 ) ( 5 x - 6 )}{7 x ( 5 x - 6 )}

Apply the fraction rule:

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

= \frac{7 x ^{2} - ( x - 1 ) ( 5 x - 6 )}{7 x ( 5 x - 6 )}

Simplify

7 x^{2} - (x - 1) (5 x - 6) : 2 x^{2} + 11 x - 6

= \frac{2 x ^{2} + 11 x - 6}{7 x ( 5 x - 6 )}

\frac{1}{18}

2 (x - 1) (x + 3)

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

\frac{7}{- 4}

\frac{121}{144}

What is x/(5x-6)-(x-1)/(7x) ?
The solution to x/(5x-6)-(x-1)/(7x) is (2x^2+11x-6)/(7x(5x-6))