Câu 1:

a)Ta có:

Tử số

$=23\times50-15$

$=23\times(48+2)-15$

$=23\times48+23\times2-15$

$=23\times48+46-15$

$=23\times48+31$

$=$Mẫu số

Vậy $\dfrac{23\times50-15}{31+23\times48}=1$ 

b)

Tử số:$23\times50+27$

$=23\times(49+1)+27$
$=23\times49+23+27$

$=23\times49+50$

Mẫu số: $1+24\times49$

$=1+(23+1)\times49$

$=1+1\times49+23\times49$

$=50+23\times49$

$=$ Tử số

Vậy $\dfrac{23\times50+27}{1+24\times49}=1$ 

c) Ta có:

Mẫu số

$=1785\times750-419$

$=1785\times(747+3)-419$

$=1785\times747+1785\times3-419$

$=1785\times747+5355-419$

$=1785\times747+4936$

$=$ Tử số 

Vậy $\dfrac{1785\times747+4936}{1785\times750-419}=1$ 

d) Ta có:

Tử số:

$=2010\times2011-1010$

$=2010\times(2009+2)-1010$

$=2010\times2009+2010\times2-1010$

$=2010\times2009+4020-1010$

$=2010\times2009+3010$

$=$ Mẫu số

Vậy $\dfrac{2010\times2011-1010}{3010+2010\times2009}=1$ 

Bài 2:

a) Ta có:

Tử số:

$=592\times105-1624$

$=592\times(95+10)-1624$

$=592\times95+592\times10-1624$

$=592\times95+5920-1624$
$=592\times95+4296$

$=$ Mẫu số

Vậy $\dfrac{592\times105-1624}{592\times95+4296}=1$ 

b) Ta có:

Tử số:

$=472\times1248+944$
$=472\times1248+472\times2$

$=472\times(1248+2)$

$=472\times1250$

$=$ Mẫu số

Vậy $\dfrac{472\times1248+944}{1250\times472}=1$ 

c)Ta có:

Mẫu số: 

$=140\times247-569$
$=(136+4)\times247-569$

$=136\times247+4\times247-569$

$=136\times247+988-569$

$=136\times247+419$

$=$ Tử số 

Vậy $\dfrac{136\times247+419}{140\times247-569}=1$ 

d) Ta có:

Tử số: 

$=5275\times654+38$

$=(5272+3)\times654+38$
$=5272\times654+3\times654+38$
$=5272\times654+1962+38$

$=5272\times654+2000$

$=$ Mẫu số 

Vậy $\dfrac{5275\times654+38}{2000+654\times5272}=1$