Find (x+y)÷(x-y), if (i) x = 2/3,y = 3/2 (ii) x = 2/5, y = 1/2 (iii) x = 5/4, y = -1/3 (iv) x = 2/7, y = 4/3

Question

Find (x+y)÷(x-y), if

(i) x = \(\frac{2}{3}\),y = \(\frac{3}{2}\)

(ii)  x = \(\frac{2}{5}\),y = \(\frac{1}{2}\)

(iii)  x = \(\frac{5}{4}\),y = \(\frac{-1}{3}\)

(iv)  x = \(\frac{2}{7}\),y = \(\frac{4}{3}\)

(v)  x = \(\frac{1}{4}\),y = \(\frac{3}{2}\)

Answer 1

(i) \((x+y)÷(x-y) \)

When,

x = \(\frac{2}{3}\), y = \(\frac{3}{2}\)

= \(\frac{\frac{2}{3}+\frac{3}{2}}{\frac{2}{3}-\frac{3}{2}}\)

= \(\frac{\frac{4+9}{6}}{\frac{4-9}{6}}\)

= \(\frac{-13}{5}\)

(ii) \((x+y)÷(x-y) \)

When,

x = \(\frac{2}{5}\), y = \(\frac{1}{2}\)

= \(\frac{\frac{2}{5}+\frac{1}{2}}{\frac{2}{5}-\frac{1}{2}}\)

= \(\frac{\frac{4+5}{10}}{\frac{4-5}{10}}\)

= \(\frac{-9}{1}\)

= -9

(iii) \((x+y)÷(x-y) \)

When,

x = \(\frac{5}{4}\), y = \(\frac{-1}{3}\)

= \(\frac{\frac{5}{4}+\frac{-1}{3}}{\frac{5}{4}-\frac{-1}{3}}\)

= \(\frac{\frac{15-4}{12}}{\frac{15+4}{12}}\)

= \(\frac{11}{19}\)

(iv) \((x+y)÷(x-y) \)

When,

x = \(\frac{2}{7}\), y = \(\frac{4}{3}\)

= \(\frac{\frac{2}{7}+\frac{4}{3}}{\frac{2}{7}-\frac{4}{3}}\)

= \(\frac{\frac{6+28}{21}}{\frac{6-28}{21}}\)

= \(\frac{-17}{11}\)

(v) \((x+y)÷(x-y) \)

When,

x = \(\frac{1}{4}\), y = \(\frac{3}{2}\)

= \(\frac{\frac{1}{4}+\frac{3}{2}}{\frac{1}{4}-\frac{3}{2}}\)

= \(\frac{\frac{1+6}{4}}{\frac{1-6}{4}}\)

= \(\frac{-7}{5}\)