When dividing fractions, it may seem to be easier if you change the sign to multiply and flip the fraction on the right side. You would then end up with:
[tex] \frac{x+4}{x} * \frac{x}{3} [/tex]
We know that when you multiply fractions, you multiply straight across the fraction bar. You would then get the following:
[tex] \frac{(x+4)*x}{x*3} [/tex]
Which you could then simplify to:
[tex] \frac{ x^{2} +4x}{3x} [/tex]
This can even futher be simplified since you have 2 terms in the numerator and 1 term in the denominator:
[tex] \frac{ x^{2} }{3x} + \frac{4x}{3x} [/tex]
When you have variables that are the same, such as in the first term, and you are dividing these terms, you subtract the exponents of the variable - in this case x:
[tex] \frac{x}{3} [/tex]
And for your second term, since both the numerator and the denominator both have coefficients multiplied by an x, the x's cancel out. So you get:
[tex] \frac{4}{3} [/tex]
Now, be sure to remember to add these two together, as you cannot forget about the addition sign:
[tex] \frac{x}{3}+ \frac{4}{3} [/tex]
Or, since both of the terms have the same denominator, you can add them together to produce:
[tex] \frac{x+4}{3} [/tex]
