Khẳng định nào sau đây là sai?        

a) \(\frac{7}{4} - \frac{3}{4}:\frac{{12}}{{21}}\)\( = \frac{7}{4} - \frac{3}{4}.\frac{{21}}{{12}}\)\( = \frac{7}{4} - \frac{{21}}{{16}}\)\( = \frac{7}{{16}}\).

b) \[\sqrt {\frac{4}{9}} - \left| {\frac{{ - 3}}{7}} \right|.\frac{7}{8} = \frac{2}{3} - \frac{3}{7}.\frac{7}{8} = \frac{2}{3} - \frac{3}{8} = \frac{{16}}{{24}} - \frac{9}{{24}} = \frac{5}{{24}}\].

c) \(\left( {\frac{1}{3} - \frac{3}{{10}}} \right):\frac{3}{5} + \left( {\frac{2}{3} - \frac{7}{{10}}} \right):\frac{3}{5}\)\( = \left( {\frac{1}{3} - \frac{3}{{10}}} \right).\frac{5}{3} + \left( {\frac{2}{3} - \frac{7}{{10}}} \right).\frac{5}{3}\)

\( = \left( {\frac{1}{3} - \frac{3}{{10}} + \frac{2}{3} - \frac{7}{{10}}} \right).\frac{5}{3} = \left( {1 - 1} \right).\frac{5}{3} = 0\).

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\frac{{a + b - c}}{c} = \frac{{b + c - a}}{a} = \frac{{c + a - b}}{b} = \frac{{a + b - c + b + c - a + c + a - b}}{{c + a + b}} = \frac{{a + b + c}}{{a + b + c}} = 1\)

Vì \(\frac{{a + b - c}}{c} = 1\) nên \(a + b - c = c\), suy ra \(a + b = 2c\).

Vì \(\frac{{b + c - a}}{a} = 1\) nên \(b + c - a = a\), suy ra \(b + c = 2a\).

Vì \(\frac{{c + a - b}}{b} = 1\) nên \(c + a - b = b\), suy ra \(c + a = 2b\).

Thay vào biểu thức \(P\) ta có:

\(P = \left( {1 + \frac{b}{a}} \right)\left( {1 + \frac{a}{c}} \right)\left( {1 + \frac{c}{b}} \right) = \frac{{a + b}}{a}.\frac{{c + a}}{c}.\frac{{b + c}}{b} = \frac{{2c}}{a}.\frac{{2b}}{c}.\frac{{2a}}{b} = \frac{{8abc}}{{abc}} = 8\)

Vậy \(P = 8\).