Question

Rewrite the following expression in standard form by finding common denominator and collecting like terms

Answer 1

We have the expression $\frac{2h}{3} - \frac{h}{9} + \frac{h-4}{6}$; to find the common denominator we are going to decompose each one of the denominators into prime factors, and then we are going to multiply the common factors raised to the highest power and all the non common factors.

The denominators of our fractions are 3, 6, and 9. 3 is already a prime, so we are going to let that one alone. 6 on the other hand is divisible by tow, so it can be decomposed into tow prime factors 2 and 3: $6=(2)(3)$.
9 is divisible by 3, so it can also be decomposed into tow prime factors 3 and 3: $9=(3)(3)=3^{2}$.
We have a common factor 3 in all our denominators, and among them the one raised to the highest power is $3^{2}$. On the other hand we only have one non-common factor, 2. So, our common denominator will be:
$common.denominator=(3^{2} )(2)=(9)(2)=18$ 

Now we know that the common denominator of our standard form fraction is 18, the only thing left is convert the denominators of each one of our fractions to 18 and simplify. To do that we are going to divide the common denominator by the denominator of each fraction, and then multiply the quotient by each one of the numerators:
$\frac{2h}{3} - \frac{h}{9}+ \frac{h-4}{6} = \frac{(6)(2h)-(2)(h)+3(h-4)}{18}$
$\frac{12h-2h+3h-12}{18}$
$\frac{13h-12}{18}$

Answer: $\frac{13h-12}{18}$