Đáp án:
Giải thích các bước giải:
a)
\(M=2.\frac{1}{547}.\frac{3}{211}-\frac{546}{547}.\frac{1}{211}-\frac{4}{547.211}\)
\(M=\left(2.\frac{1}{547}.\frac{3}{211}\right)-\left(\frac{546}{547}.\frac{1}{211}\right)-\left(\frac{4}{547.211}\right)\)
\(M=\frac{6}{547.211}-\frac{546}{547.211}-\frac{4}{547.211}\)
\(M=\frac{6}{115417}-\frac{546}{115417}-\frac{4}{115417}\)
\(M=\frac{-540}{115417}-\frac{4}{115417}\)
\(M=\frac{-544}{115417}\)
b)
\(N=2\frac{1}{315}.\frac{1}{651}-\frac{1}{105}.3\frac{650}{651}-\frac{4}{315.651}+\frac{4}{105}\)
\(N=\left(2+\frac{1}{315}\right).\frac{1}{651}-3.\frac{1}{315}.\left(4-\frac{1}{651}\right)-4.\frac{1}{315}.\frac{1}{651}+12.\frac{1}{315}\)
Đặt \(\frac{1}{315}=x;\frac{1}{651}=y\),khi đó P trở thành:
\(N=\left(2+x\right).y-3x.\left(4-y\right)-4xy+12y\)
\(N=2y+xy-12x+3xy-4xy+12x\)
\(N=2y=2.\frac{1}{651}=\frac{2}{651}\)
c)
Đặt \(a=\dfrac{1}{117};b=\dfrac{1}{119}\) thay vào P được:
P=\(\left(3+a\right)b-4a\left(6-b\right)-5ab+\dfrac{8}{39}\)
=\(3b+ab-24a+4ab-5ab+\dfrac{8}{39}\)
=\(3b-24a+\dfrac{8}{39}\) (1)
Thay \(a=\dfrac{1}{117};b=\dfrac{1}{119}\) vào (1) ta đuợc:
P=\(\dfrac{3}{119}-\dfrac{24}{117}+\dfrac{8}{39}=\dfrac{3}{119}-0=\dfrac{3}{119}\)
d)
Đặt :
\(\frac{1}{315}=a;\frac{1}{651}=b\) thay vào Q ta được :
\(Q=\left(2+a\right)b-\left(3+1-b\right).3a-4ab+12a\)
\(\Leftrightarrow Q=2b+ab-12a+3ab-4ab+12a\)
\(\Leftrightarrow Q=2b\)
Thay \(b=\frac{1}{651}\) ta được :
\(Q=\frac{2}{651}\)
