a:b barabar c:d to ma+nc/mb+nd
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a/b = c /d
ma /mb = nc/ nd
ma/nc = mb/nd --- 1)
Now, ma+nc = nc ( 1+ ma/nc) = nc (1+mb/nd) ----- 2)
mb+ nd = nd (1+ mb/nd) --- 3)
2 / 3
nc (1+mb/nd) / nd (1+mb/nd) = nc/nd = c/d =a/b
ma /mb = nc/ nd
ma/nc = mb/nd --- 1)
Now, ma+nc = nc ( 1+ ma/nc) = nc (1+mb/nd) ----- 2)
mb+ nd = nd (1+ mb/nd) --- 3)
2 / 3
nc (1+mb/nd) / nd (1+mb/nd) = nc/nd = c/d =a/b
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