Problem 1 Adding Expressions With Like Denominators

What is the sum?

1. 4 3 y + 7 3 y fraction 4 , over 3 y end fraction , plus , fraction 7 , over 3 y end fraction

   4 3 y + 7 3 y = 4 + 7 3 y Add the numerators .   = 11 3 y Simplify the numerator . table with 2 rows and 3 columns , row1 column 1 , fraction 4 , over 3 y end fraction , plus , fraction 7 , over 3 y end fraction , column 2 equals . fraction 4 plus 7 , over 3 y end fraction , column 3 cap addthenumerators . . , row2 column 1 , , column 2 equals , fraction 11 , over 3 y end fraction , column 3 cap simplifythenumerator . . , end table

   Think

   Once you are comfortable adding rational expressions with like denominators, you can add the numerators and simplify all in one step.

2. 3 x x − 2 + x x − 2 fraction 3 x , over x minus 2 end fraction . plus . fraction x , over x minus 2 end fraction

   3 x x − 2 + x x − 2 = 3 x + x x − 2 Add the numerators .   = 4 x x − 2 Simplify the numerator . table with 2 rows and 3 columns , row1 column 1 , fraction 3 x , over x minus 2 end fraction . plus . fraction x , over x minus 2 end fraction , column 2 equals . fraction 3 x plus x , over x minus 2 end fraction , column 3 cap addthenumerators . . , row2 column 1 , , column 2 equals . fraction 4 x , over x minus 2 end fraction , column 3 cap simplifythenumerator . . , end table

✓ Got It?

1. What is the sum 2 a 3 a − 4 + 3 a 3 a − 4 ? fraction 2 eh , over 3 eh minus 4 end fraction . plus . fraction 3 eh , over 3 eh minus 4 end fraction . question mark