3+a/b=3.a/b

3=2.a/b

a/b=3/2

a)p(x)=x⁷-80x⁶+80x⁵-80x⁴+.........+80+15

=x⁷-(79+1)⁶+(79+1)⁵-(79+1)⁴+.........+(79+1)x+15

mà x=79

=> x⁷-(x+1)⁶+(x+1)⁵-(x+1)⁴+..........+(x+1)x+15

=x⁷-x⁷+x⁶-x⁶+x⁵-x⁵+........+x²+x+15

=x+15

=79+15

=94

A=374-42385-819+823

A= -42011-819+823

A=-42830+823

A=-42004

\(C=\frac{4-3x}{2x+5}\inℤ\Rightarrow2C=\frac{8-6x}{2x+5}=\frac{23-15-6x}{2x+5}=\frac{23}{2x+5}-3\inℤ\)

\(\Rightarrow\frac{23}{2x+5}\inℤ\)mà \(x\inℤ\)nên \(2x+5\inƯ\left(23\right)=\left\{-23,-1,1,23\right\}\Leftrightarrow x\in\left\{-14,-3,-2,9\right\}\).

Thử lại đều thỏa mãn. 

\(D=\frac{x^2-3x+7}{x-3}=x+\frac{7}{x-3}\inℤ\)mà \(x\inℤ\)nên \(x-3\inƯ\left(7\right)=\left\{-7,-1,1,7\right\}\)

\(\Leftrightarrow x\in\left\{-4,2,4,10\right\}\).

\(E=\frac{x^2+1}{x-1}=\frac{x^2-1+2}{x-1}=x+1+\frac{2}{x-1}\)

Tiếp tuc bạn làm tương tự ý \(D\).

\(A=\frac{\frac{-4}{5}+\frac{4}{19}-\frac{4}{23}}{\frac{8}{5}-\frac{8}{19}+\frac{8}{23}}=\frac{-\left(\frac{4}{5}-\frac{4}{19}+\frac{4}{23}\right)}{2\left(\frac{4}{5}-\frac{4}{19}+\frac{4}{23}\right)}=-\frac{1}{2}\)

\(\left(-1\frac{1}{2}\right)\left(-1\frac{1}{3}\right)\left(-1\frac{1}{4}\right)...\left(-1\frac{1}{2003}\right)\left(-1\frac{1}{2004}\right)\)

\(=-\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.....\frac{2004}{2003}.\frac{2005}{2004}\)

\(=-\frac{3.4.5.....2004.2005}{2.3.4.....2003.2004}=\frac{-2005}{2}\)