Question 203372
The easiest way to simplify complex fractions is to:
Multiply the numerator and denominator of the "big" fraction by the Lowest Common Denominator of all the "little" fractions which are in the "big" fraction.
{{{(2+ 1/(4a))/(2/a-a)}}}
The "little" fractions are {{{1/(4a)}}} and {{{2/a}}}. The LCD of these two is: 4a. So we will multiply the numerator and denominator of the "big" fraction by 4a:
{{{((2+ 1/(4a))/(2/a-a))((4a)/(4a))}}}
Using the Distributive Property to multiply the two numerators and the two denominators:
{{{(2(4a) + (1/(4a))(4a))/((2/a)(4a)-a(4a))}}}
Simplify:
{{{(8a + (1/(cross(4a)))cross(4a))/((2/(cross(a)))(4*cross(a))- 4a^2))}}}
{{{(8a + 1)/(2*4 - 4a^2)}}}
{{{(8a + 1)/(8 - 4a^2)}}}<br>
Problem: {{{(n/12- 2/9)/(n/6)}}}
The LCD of the "little" fractions is 36. So we will multiply the numerator and denominator of the "big" fraction by 36:
{{{((n/12- 2/9)/(n/6))(36/36)}}}
{{{((n/12)36 - (2/9)(36))/((n/6)36)}}}
{{{(3n - 8)/(6n)}}}<br>
Problem: {{{(x/2+x/3)/(x/4)}}}
The LCD of the "little" fractions is: 12. So we will multiply the numerator and denominator of the "big" fraction by 12:
{{{((x/2+x/3)/(x/4))(12/12)}}}
{{{((x/2)12 + (x/3)12)/((x/4)12)}}}
{{{(6x + 4x)/(3x)}}}
{{{(10x)/(3x)}}}
{{{10/3}}}<br>
Now that you've seen several examples, I'll leave the rest for you.