Question

hw 12.2_add & subtract rational expressions
score: 2/17 answered: 2/17
question 3
add or subtract
\\(\frac{9}{7} + \frac{3}{7} = \square\\)
\\(\frac{7}{2} - \frac{9}{2} = \square\\)
\\(\frac{7}{2} + \frac{3}{5} = \square\\)
\\(\frac{5}{8} - \frac{2}{7} = \square\\)

Explanation:

Step1: Add numerators, same denominator

$\frac{9}{7} + \frac{3}{7} = \frac{9+3}{7} = \frac{12}{7}$

Step2: Subtract numerators, same denominator

$\frac{7}{2} - \frac{9}{2} = \frac{7-9}{2} = \frac{-2}{2} = -1$

Step3: Find common denominator, add

Common denominator of 2 and 5 is 10.
$\frac{7}{2} + \frac{3}{5} = \frac{7\times5}{2\times5} + \frac{3\times2}{5\times2} = \frac{35}{10} + \frac{6}{10} = \frac{35+6}{10} = \frac{41}{10}$

Step4: Find common denominator, subtract

Common denominator of 8 and 7 is 56.
$\frac{5}{8} - \frac{2}{7} = \frac{5\times7}{8\times7} - \frac{2\times8}{7\times8} = \frac{35}{56} - \frac{16}{56} = \frac{35-16}{56} = \frac{19}{56}$

Answer:

$\frac{12}{7}$
$-1$
$\frac{41}{10}$
$\frac{19}{56}$