How can I solve the equation (2x - 1) / (x + 4) - (2x - 5) / (x + 3) = 0

Answer:
We have 

$\frac{\left( 2x - 1 \right)}{\left( x + 4 \right)} - \frac{\left( 2x - 5\right)}{\left( x + 3 \right)}$ = 0

Taking L.C.M. we get

$\Rightarrow$$\frac{\left( 2x - 1 \right) \left( x + 3 \right) - \left( 2x - 5\right) \left( x + 4 \right)}{\left( x + 4 \right) \left( x + 3 \right)}$ = 0

Multiply the numerator terms

$\Rightarrow$ $\frac{\left( 2x^2 + 6x - x - 3 \right) - \left( 2x^2 +8x - 5x - 20\right) }{\left( x + 4 \right) \left( x + 3 \right)}$ = 0

Now we can send our denominator at L.H.S. As :

$\Rightarrow$ ( 2 x² + 5 x - 3 ) - ( 2 x² + 3 x - 20 ) = 0 [ ( x + 4 ) ( x + 3 ) ]

$\Rightarrow$ ( 2 x² + 5 x - 3 ) - ( 2 x² + 3 x - 20 ) = 0 

$\Rightarrow$ ( 2 x² + 5 x - 3  - 2 x² - 3 x + 20 ) = 0 

$\Rightarrow$ ( 2 x + 17 ) = 0 

$\Rightarrow$ 2 x = - 17

$\Rightarrow$ x  = $-\frac{17}{2}$                              ( Ans )