\(\frac{\frac{1}{6}+\frac{1}{10}+\frac{1}{15}}{\frac{1}{6}+\frac{1}{10}-\frac{1}{15}}=\frac{\frac{5+3+2}{30}}{\frac{5+3-2}{30}}=\frac{\frac{1}{3}}{\frac{1}{5}}=1\frac{2}{3}\)

\(\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}}{\frac{1}{4}-\frac{1}{6}}=\frac{\frac{30-20+15-12}{60}}{\frac{3-2}{12}}=\frac{\frac{13}{60}}{\frac{1}{12}}=2\frac{3}{5}\)

tíc nha mn, mình đang bị âm điểm

thank you ban nha

a (1/6 + 1/10 + 1/15) : (1/6 + 1/10 - 1/15)

= ( 5/30 + 3/30 + 2/30) : (5/30 + 3/30 - 2/30)

= 1/3 : 1/6 = 1/3 x 6/1 = 6/3 = 2

b (1/2 - 1/3 + 1/4 - 1/5) : (1/4 - 1/5)

= (1/2 - 1/3 + 1/4 - 1/5) : (1/4 - 1/5)

= 1/2 - 1/3 = 1/6

a)  

(1/6+1/10+1/15) : (1/6+1/10-1/15)

= (1/6+1/10): (1/6+1/10)

= 4/15:4/15

=1

~Hy

3 x 15 + 21 x 15 + 85 x 5

= 45 + 315 + 425

= 785

15 - 30 + 40 

= 25

21 + 19 - 50 + 10

= 0

\(\dfrac{1}{5}-\dfrac{1}{4}+2\)

\(=-\dfrac{1}{20}+2\)

\(=\dfrac{39}{20}\)

\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)

\(=\dfrac{5}{12}\times\dfrac{1}{4}\)

\(=\dfrac{5}{12}\times\dfrac{3}{12}\)

\(=\dfrac{5}{48}\)

\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)

\(=-\dfrac{9}{20}\)

\(3\times15+21\times15+85\times5\\ =15\times\left(3+21\right)+425\\ =15\times24+425\\ =360+425\\ =785\)

\(15-30+40\\ =\left(15+40\right)-30\\ =55-30\\ =25\)

\(21+19-50+10\\ =\left(21+19\right)-\left(50-10\right)\\ =40-40\\ =0\)

\(\dfrac{1}{5}-\dfrac{1}{4}+2\)

\(=\dfrac{4}{20}-\dfrac{5}{20}+\dfrac{40}{20}\)

\(=\dfrac{\left(4+40\right)}{20}-\dfrac{5}{20}\)

\(=\dfrac{44}{20}-\dfrac{5}{20}\)

\(=\dfrac{39}{20}\)

\(\left(\dfrac{1}{4}+\dfrac{1}{6}\right)\times\left(\dfrac{1}{2}-\dfrac{1}{4}\right)\)

\(=\dfrac{5}{12}\times\dfrac{1}{4}\)

\(=\dfrac{5}{48}\)

\(\dfrac{1}{10}+\dfrac{1}{5}-\dfrac{3}{4}\)

\(=\dfrac{2}{20}+\dfrac{4}{20}-\dfrac{15}{20}\)

\(=\dfrac{6}{20}-\dfrac{15}{20}\)

\(=-\dfrac{9}{20}\)

\(\dfrac{\left(\dfrac{5}{30}+\dfrac{3}{30}+\dfrac{2}{30}\right):\left(\dfrac{5}{30}+\dfrac{3}{30}-\dfrac{2}{30}\right)}{\left(\dfrac{30}{60}-\dfrac{20}{60}+\dfrac{15}{60}-\dfrac{12}{60}\right):\left(\dfrac{3}{12}-\dfrac{2}{12}\right)}=\dfrac{\dfrac{1}{3}:\dfrac{1}{5}}{\dfrac{13}{60}:\dfrac{1}{12}}=\dfrac{\dfrac{1}{3}\times5}{\dfrac{13}{60}\times12}=\dfrac{\dfrac{5}{3}}{\dfrac{13}{5}}=\dfrac{25}{39}\)

=\(\dfrac{\dfrac{1}{3}:\dfrac{1}{5}}{\dfrac{13}{60}:\dfrac{1}{12}}=\dfrac{\dfrac{5}{3}}{\dfrac{13}{5}}=\dfrac{25}{39}\)

Bài 1:

a) [ (1/6 + 1/10 + 1/15) : (1/6 + 1/10 - 1/15) phần 1/2 - 1/3 + 1/4 - 1/5 ] : (1/4 - 1/6)

= [ (1/6 : 1/6) + (1/10 : 1/10) - (1/15 : 1/15) phần 30/60 - 20/60 + 15/60 - 12/60 ] : (3/12 - 2/12)

= [ 1 + 1 - 1 phần 13/60 ] : 1/12

= [ 1 : 13/60 ] x 12

= 60/13 x 12

=720/ 13

b) (3/20 + 1/2 - 1/15) x 12/49 phần 3 và 1/3 + 2/9

= (9/60 + 30/60 - 4/60) x 12/49 phần 10/3 + 2/9

= 7/12 x 12/49 phần 30/9 + 2/9

= 1/7 : 32/9

= 1/7 x 9/32

= 9/224

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

1.3.77−1​+3.7.99−3​+7.9.1313−7​+9.13.1515−9​+\frac{19-13}{13.15.19}+13.15.1919−13​

=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}=1.31​−3.71​+3.71​−7.91​+7.91​−9.131​+9.131​−13.151​+13.151​−15.191​

=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}=1.31​−15.191​=28595​−2851​=28594​

b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)b,=61​.(1.3.76​+3.7.96​+7.9.136​+9.13.156​+13.15.196​)

làm giống như trên

c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)c,=81​.(1.2.31​+2.3.41​+3.4.51​+...+48.49.501​)

=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)=161​.(1.2.32​+2.3.42​+3.4.52​+...+48.49.502​)

=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)=161​.(1.2.33−1​+2.3.44−2​+3.4.55−3​+...+48.49.5050−48​)

=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)=161​.(1.21​−2.31​+2.31​−3.41​+3.41​−4.51​+...+48.491​−49.501​)

=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}=161​.(21​−24501​)=161​.(24501225​−24501​)=4900153​

d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)d,=75​.(1.5.87​+5.8.127​+8.12.157​+...+33.36.407​)

=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)=75​.(1.5.88−1​+5.8.1212−5​+8.12.1515−8​+...+33.36.4040−33​)

=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)=75​.(1.51​−5.81​+5.81​−8.121​+8.121​−12.151​+...+33.361​−36.401​)

=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}=75​.(51​−14401​)=75​.(1440288​−14401​)=28841​

P/S: . là nhân nha