Given:
Expression is
[tex]\dfrac{\dfrac{1}{x-3}+\dfrac{4}{x}}{\dfrac{4}{x}-\dfrac{1}{x-3}}[/tex]
To find:
The simplified form of given expression.
Solution:
We have,
[tex]\dfrac{\dfrac{1}{x-3}+\dfrac{4}{x}}{\dfrac{4}{x}-\dfrac{1}{x-3}}[/tex]
[tex]=\dfrac{\dfrac{1(x)+4(x-3)}{(x-3)x}}{\dfrac{4(x-3)-1(x)}{x(x-3)}}[/tex]
[tex]=\dfrac{x+4x-12}{(x-3)x}\times \dfrac{x(x-3)}{4x-12-x}[/tex]
[tex]=\dfrac{5x-12}{3x-12}[/tex]
[tex]=\dfrac{5x-12}{3(x-4)}[/tex]
Therefore, the last option is correct, i.e., [tex]\dfrac{5x-12}{3(x-4)}[/tex].
