What is x/(2x-9)-(x-3)/(4x) ?

The solution to x/(2x-9)-(x-3)/(4x) is (2x^2+15x-27)/(4x(2x-9))

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simplify x/(2x-9)-(x-3)/(4x)

simplify

\frac{x}{2 x - 9} - \frac{x - 3}{4 x}

\frac{2 x ^{2} + 15 x - 27}{4 x ( 2 x - 9 )}

Solution steps

\frac{x}{2 x - 9} - \frac{x - 3}{4 x}

Least Common Multiplier of

2 x - 9, 4 x : 4 x (2 x - 9)

Adjust Fractions based on the LCM

= \frac{4 x ^{2}}{4 x ( 2 x - 9 )} - \frac{( x - 3 ) ( 2 x - 9 )}{4 x ( 2 x - 9 )}

Apply the fraction rule:

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

= \frac{4 x ^{2} - ( x - 3 ) ( 2 x - 9 )}{4 x ( 2 x - 9 )}

Simplify

4 x^{2} - (x - 3) (2 x - 9) : 2 x^{2} + 15 x - 27

= \frac{2 x ^{2} + 15 x - 27}{4 x ( 2 x - 9 )}

(3 - 16) (- 9 - 100)

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

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

(- 43)^{2}

11. 5^{2}

What is x/(2x-9)-(x-3)/(4x) ?
The solution to x/(2x-9)-(x-3)/(4x) is (2x^2+15x-27)/(4x(2x-9))