Adding and Subtracting Fractions with Unlike Denominators Fractions



To add or subtract two fractions with unlike denominator we 
Find the LCD (Least Common Denominator) for each fraction. 
Express each fraction as an equivalent fraction whose denominator
is the LCD for the two fractions. 
Add the fractions. 

Examples: 
2/9 + 1/6                                             LCD is 18.

=[2(2)]/[9(2)] + [1(3)]/[6(3)]

= 4/18 + 3/18

= 7/18 
5/[3a] + 1/[12ab]                               LCD is 12ab.

= [5(4b)/[3a(4b)] + 1/[12ab]

= [20b]/[12ab] + 1/[12ab]

= [20b + 1]/[12ab] 
[2x]/[x²  + 4x + 4] + 3/[x²  - 4]

= [2x]/[[(x + 2)² ] + 3/[(x + 2)(x - 2)]    LCD is (x + 2)² (x - 2).  

= [2x(x - 2)/[(x + 2)² (x - 2)] + [3(x + 2)]/[(x + 2)² (x - 2)]

= [2x² - 4x]/[(x + 2)² (x - 2)] + [3x + 6]/[(x + 2)² (x - 2)]

= [(2x² - 4x)+(3x + 6)]/[(x + 2)² (x - 2)]

= [2x² - 4x + 3x + 6]/[(x + 2)² (x - 2)]

= [2x² - x + 6]/[(x + 2)² (x - 2)]