\(\frac{1995.1993-18}{1975.1993.1994}\)\(=\frac{1995-18}{1975.1994}\)

                                      \(=\frac{1977}{1975.1994}\)

                                      \(=\frac{1975+2}{1975.1994}\)

                                      \(=\frac{2}{1994}=\frac{1}{997}\)

\(\frac{1996.1995-996}{1000+1996.1994}\)\(=\frac{1995-996}{1994+1000}\)

                                           \(=\frac{999}{1994+1000}\)

                                           \(=\frac{999}{1994+999+1}\)

                                          \(=\frac{1}{1994+1}=\frac{1}{1995}\)

1996*1995-1996*1994=1996

(1996*1995-996)-(1996*1994)=1996-996=1000

(1996*1995-996)-(1996*1994+1000)=1996-996-1000=0

=>(1996*1995-996)/(1996*1994+1000)=1( vì tử số bằng mẫu số)

\(\frac{1996.1995-996}{1996.1994+1000}=\frac{\left(1000+996\right).1995-996}{\left(1000+996\right).1994+1000}\)

\(=\frac{1000.1995+996.1995-996}{996.1994+1000.1994+1000}=\frac{1000.1995+996\left(1995-1\right)}{996.1994+1000\left(1994+1\right)}\)

\(=\frac{1000.1995+996.1994}{996.1994+1000.1995}\)=1

\(\frac{1996\cdot1995-996}{1996\cdot1994+1000}\)

\(=\frac{1996\cdot\left(1994+1\right)-996}{1996\cdot1994+1000}\)

\(=\frac{1996\cdot1994+\left(1996-996\right)}{1996\cdot1994+1000}\)

\(=\frac{1996\cdot1994+1000}{1996\cdot1994+1000}\)

\(=1\)

\(\dfrac{1996.1995-996}{1000+1996.1994}=\dfrac{1996\left(1994+1\right)-996}{1000+1996.1994}=\dfrac{1996.1994+1996-996}{1000+1996.1994}\) 

\(=\dfrac{1000+1996.1994}{1000+1996.1994}=1\)

1)

a) \(\left(-48\right)^3:16^3\)

\(=\left(-48:16\right)^3\)

\(=\left(-3\right)^3\)

\(=-27.\)

b) \(\left(\frac{9}{10}\right)^6:\left(\frac{17}{-20}\right)^6\)

\(=\left(\frac{9}{10}:\frac{17}{-20}\right)^6\)

\(=\left(-\frac{18}{17}\right)^6\)

Chúc em học tốt!

\(\frac{-13^3}{\left(2^3\right)^3}:\frac{\left(-2^5\right)^4}{13^4}\)1.

a, (-48)³:16³

= \(\left(\frac{-48}{16}\right)^3\)

= (-3)³

b,\(\left(\frac{9}{10}\right)^6\):\(\left(\frac{17}{-20}\right)^6\)

= \(\left(\frac{9}{10}:\frac{17}{-20}\right)^6\)

=\(\left(\frac{-18}{17}\right)^6\)

c, \(\left(\frac{-13}{8}\right)^3:\left(\frac{-32}{13}\right)^4\)

= \(\frac{-13^3}{\left(2^3\right)^3}:\frac{\left(-2^5\right)^4}{13^4}\)

= \(\frac{-13^3}{2^9}.\frac{-13^4}{2^{20}}\)

=\(\frac{13^7}{2^{29}}\)

Lời giải:

\(M=\frac{ab}{(c-a)(c-b)}+\frac{ac}{(b-a)(b-c)}+\frac{bc}{(a-b)(a-c)}\\ =\frac{-ab(a-b)}{(a-b)(b-c)(c-a)}+\frac{-ac(c-a)}{(a-b)(b-c)(c-a)}+\frac{-bc(b-c)}{(a-b)(b-c)(c-a)}\\ =\frac{-[ab(a-b)+ac(c-a)+bc(b-c)]}{(a-b)(b-c)(c-a)}\\ =\frac{(ab^2+bc^2+ca^2)-(a^2b+b^2c+c^2a)}{(ab^2+bc^2+ca^2)-(a^2b+b^2c+c^2a)}=1\)

tham khao nha

\(A=\left(\frac{\sqrt{a}}{\sqrt{ab}-b}+\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{ab}-a}\right):\left(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}}\right)\)

\(A=\left(\frac{\sqrt{a}}{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}+\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{a}\left(\sqrt{b}-\sqrt{a}\right)}\right):\left(\frac{\sqrt{b}+\sqrt{a}}{\sqrt{ab}}\right)\)

\(A=\left(\frac{\sqrt{a}}{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}-\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}\right).\frac{\sqrt{ab}}{\sqrt{b}+\sqrt{a}}\)

\(A=\frac{a-2\sqrt{ab}+b}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}.\frac{\sqrt{ab}}{\sqrt{b}+\sqrt{a}}\)

\(A=\frac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}.\frac{\sqrt{ab}}{\sqrt{b}+\sqrt{a}}\)

\(A=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)

vay \(A=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)

ĐK : tự ghi nha

\(\left(\frac{\sqrt{a}}{\sqrt{ab}-b}+\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{ab}-a}\right):\left(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}}\right)\)

thiếu điều kiện kìa @Despacito