Answer:
[tex]\frac{7x^2-7x+12}{2x(x-4)}[/tex]
Step-by-step explanation:
Given
[tex]\frac{3x}{x-4}[/tex] + [tex]\frac{x-3}{2x}[/tex]
Before we can add the fractions we require them to have a common denominator.
Multiply the numerator/denominator of the left fraction by 2x
Multiply the numerator/denominator of the right fraction by (x - 4)
= [tex]\frac{3x(2x)}{2x(x-4)}[/tex] + [tex]\frac{(x-3)(x-4)}{2x(x-4)}[/tex]
Distribute and simplify the numerators leaving the denominator
= [tex]\frac{6x^2+x^2-7x+12}{2x(x-4)}[/tex]
= [tex]\frac{7x^2-7x+12}{2x(x-4)}[/tex]
