For this question, you have to take Least Common Multiplier for which in this case will be "45" as, the denominators can get similar and get multiplied by a same value to form a similar expression. This allows us to cancel out them by common factors. Full process shown below.
[tex]\mathbf{Given \: \: Expression: \: \dfrac{x - 4}{5} = 9 - \dfrac{2x - 41}{9}}[/tex]
[tex]\mathbf{\dfrac{x - 4}{5} \times 45 = 9 \times 45 - \dfrac{2x - 41}{9} \times 45}[/tex]
[tex]\mathbf{9(x - 4) = 405 - 5 (2x - 41)}[/tex]
[tex]\mathbf{9x - 36 = 405 - 10x + 205}[/tex]
[tex]\mathbf{9x - 36 = - 10x + 610}[/tex]
[tex]\mathbf{9x - 36 + 36 = - 10x + 610 + 36}[/tex]
[tex]\mathbf{9x = - 10x + 646}[/tex]
[tex]\mathbf{9x + 10x = - 10x + 646 + 10x}[/tex]
[tex]\mathbf{19x = 646}[/tex]
[tex]\mathbf{\dfrac{19x}{19} = \dfrac{646}{19}}[/tex]
[tex]\mathbf{\therefore \quad x = 34}[/tex]
[tex]\boxed{\mathbf{\underline{\therefore \quad Final \: \: Answer \: \: is; \: \: x = 34}}}[/tex]
Hope it helps.
