Findx+y÷x−yifi x=23y=32ii x=25y=12iii x=54y=−13ivx=27y=

SOLUTION

(i) $x=\frac{2}{3},y=\frac{3}{2}$ $\therefore x+y=\frac{2}{3}+\frac{3}{2}=\frac{4+9}{6}=\frac{13}{6}andx-y=\frac{2}{3}-\frac{3}{2}=\frac{4-9}{6}=\frac{-5}{6}Now(x+y)÷(x-y)=\frac{13}{6}+\frac{-5}{6}=\frac{13}{6}\times \frac{6}{-5}=\frac{13}{-5}=\frac{13\times (-1)}{-5\times (-1)}=\frac{-13}{5}$

(ii) $x=\frac{2}{5},y=\frac{1}{2}$ $\therefore x+y=\frac{2}{5}+\frac{1}{2}=\frac{4+5}{10}=\frac{9}{10}x-y=\frac{2}{5}-\frac{1}{2}=\frac{4-5}{10}=\frac{-1}{10}\therefore (x+y)÷(x-y)=\frac{9}{10}÷\frac{-1}{10}=\frac{9}{10}\times \frac{10}{-1}=\frac{9}{-1}=-9$

(iii) $x=\frac{5}{4},y=\frac{-1}{3}$ $\therefore x+y=\frac{5}{4}+\frac{-1}{3}=\frac{15-4}{12}=\frac{11}{12}x-y=\frac{5}{4}-\frac{-1}{3}=\frac{15+4}{12}=\frac{19}{12}\therefore (x+y)÷(x-y)=\frac{11}{12}÷\frac{19}{12}=\frac{11}{12}\times \frac{12}{19}=\frac{11}{19}$

(iv)$x=\frac{2}{7},y=\frac{4}{3}$ $\therefore x+y=\frac{2}{7}+\frac{4}{3}=\frac{6+28}{21}=\frac{34}{21}x-y=\frac{2}{7}-\frac{4}{3}\frac{6-28}{21}=\frac{-22}{21}\therefore (x+y)÷(x-y)=\frac{34}{21}÷\frac{-22}{21}=\frac{34}{21}\times \frac{21}{-22}=\frac{17\times 1}{1\times (-11)}=\frac{17}{-11}=\frac{17\times (-1)}{-11\times (-1)}=\frac{-17}{11}$

(v) $x=\frac{1}{4},y=\frac{3}{2}$ $x+y=\frac{1}{4}+\frac{3}{2}=\frac{1+6}{4}=\frac{7}{4}x-y=\frac{1}{4}-\frac{3}{2}=\frac{1-6}{4}=\frac{-5}{4}\therefore (x+y)÷(x-y)=\frac{7}{4}÷\left(\frac{-5}{4}\right)=\frac{7}{4}\times \frac{4}{-5}=\frac{7}{-5}=\frac{7\times (-1)}{-5\times (-1)}=\frac{-7}{5}$