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

The solution to (x-4)/(2x)+(2x+3)/(2x-3) is (6x^2-5x+12)/(2x(2x-3))

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

simplify

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

\frac{6 x ^{2} - 5 x + 12}{2 x ( 2 x - 3 )}

Solution steps

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

Least Common Multiplier of

2 x, 2 x - 3 : 2 x (2 x - 3)

Adjust Fractions based on the LCM

= \frac{( x - 4 ) ( 2 x - 3 )}{2 x ( 2 x - 3 )} + \frac{( 2 x + 3 ) \cdot 2 x}{2 x ( 2 x - 3 )}

Apply the fraction rule:

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

= \frac{( x - 4 ) ( 2 x - 3 ) + ( 2 x + 3 ) \cdot 2 x}{2 x ( 2 x - 3 )}

Simplify

(x - 4) (2 x - 3) + (2 x + 3) \cdot 2 x : 6 x^{2} - 5 x + 12

= \frac{6 x ^{2} - 5 x + 12}{2 x ( 2 x - 3 )}

3 \times \frac{2}{4}

- 108 \div 12

8 x^{2} - 6 x - 27

\frac{3}{x - 4}

7 0^{2} + 10 0^{2}

What is (x-4)/(2x)+(2x+3)/(2x-3) ?
The solution to (x-4)/(2x)+(2x+3)/(2x-3) is (6x^2-5x+12)/(2x(2x-3))