Bài 2:

a: \(\Leftrightarrow x:\dfrac{4}{5}=\dfrac{-4}{6}+\dfrac{3}{6}=\dfrac{-1}{6}\)

=>x=-1/6*4/5=-4/30=-2/15

b: =>1/6x=5/6-7/12+1/3=10/12-7/12+4/12=7/12

=>x=7/2

c: =(47/11-3x)*11/5=-21/5

=>47/11-3x=-21/5:11/5=-21/11

=>3x=68/11

=>x=68/33

Ta có:

\(\dfrac{1}{x-y}+\dfrac{3xy}{y^3-x^3}+\dfrac{x-y}{x^2+xy+y^2}\\ =\dfrac{x^2+xy+y^2-3xy+\left(x-y\right)^2}{x^3-y^3}\\ =\dfrac{2\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\\ =\dfrac{2\left(x-y\right)}{x^2+xy+y^2}\)

    \(\dfrac{1}{x-y}+\dfrac{3xy}{y^3-x^3}+\dfrac{x-y}{x^2+xy+y^2}\) \(=\dfrac{x^2+xy+y^2}{x^3-y^3}-\dfrac{3xy}{x^3-y^3}+\dfrac{\left(x-y\right)^2}{x^3-y^3}\)

\(=\dfrac{x^2+xy+y^2-3xy+x^2-2xy+y^2}{x^3-y^3}\)

\(=\dfrac{2x^2+2y^2-4xy}{x^3-y^3}\)

\(=\dfrac{2x^2-2xy-2xy+2y^2}{x^3-y^3}\)

\(=\dfrac{2x\left(x-y\right)-2y\left(x-y\right)}{x^3-y^3}\)

\(=\dfrac{\left(2x-2y\right)\left(x-y\right)}{\left(x-y\right)\left(x^2+xy+y^2\right)}\)

\(=\dfrac{2x-2y}{x^2+xy+y^2}\)

a. 92 + (− 22) = 70
b. (− 801) + (− 199) = -1000
c. −345 − (− 209) = -136

d. 116 − 128 = -12
e. (− 304) + 195 = -109
f. (− 457) + 457 = 0

\(=\left[\left(-6x\right)+\left(x^2+9\right)\right]\left[\left(-6x\right)-\left(x^2+9\right)\right]\)

\(=\left(-6x\right)^2-\left(x^2+9\right)^2\)

\(=36x^2-\left(x^4+18x^2+81\right)\)

\(=-x^4+18x^2-81\)

\(=-\left(x^4-18x^2+81\right)\)

\(=-\left(x^2-9\right)^2\)

Ta có: \(\left(x^2-6x+9\right)\left(-x^2-6x-9\right)\)

\(=-\left(x^2-6x+9\right)\left(x^2+6x+9\right)\)

\(=-\left[\left(x-3\right)^2\cdot\left(x+3\right)^2\right]\)

\(=-\left(x^2-9\right)^2\)

\(a,\dfrac{-13}{5}-\dfrac{-7}{15}.\dfrac{120}{63}+\dfrac{4}{5}\\ =\dfrac{-13}{5}+\dfrac{8}{9}+\dfrac{4}{5}\\ =\dfrac{-77}{45}+\dfrac{4}{5}\\ =\dfrac{-41}{45}\\ b.\left(7\dfrac{5}{9}+2\dfrac{2}{3}\right)-5\dfrac{2}{9}\\ =\left(\dfrac{68}{9}+\dfrac{8}{3}\right)-\dfrac{47}{9}\\ =\dfrac{92}{9}-\dfrac{47}{9}\\ =5\)

2)\(-\dfrac{13}{5}--\dfrac{7}{15}.\dfrac{120}{63}+\dfrac{4}{5}\)
\(=-\dfrac{13}{5}+\dfrac{7.15.8}{15.9.7}+\dfrac{4}{5}\)
\(=-\dfrac{13}{5}+\dfrac{8}{9}+\dfrac{4}{5}\)
\(=\left(-\dfrac{13}{5}+\dfrac{4}{5}\right)+\dfrac{8}{9}\)
\(=-\dfrac{9}{5}+\dfrac{8}{9}\)
\(=\dfrac{-81+40}{45}=-\dfrac{41}{45}\)
3)\(\left(7\dfrac{5}{9}+2\dfrac{2}{3}\right)-5\dfrac{2}{9}\)
\(=\left(7\dfrac{5}{9}-5\dfrac{2}{9}\right)+2\dfrac{2}{3}\)
\(=2\dfrac{1}{3}+2\dfrac{2}{3}\)
\(=5\)

a,−135−−715.12063+45=−135+89+45=−7745+45=−4145b.(759+223)−529=(689+83)−479=929−479=5a,−135−−715.12063+45=−135+89+45=−7745+45=−4145b.(759+223)−529=(689+83)−479=929−479=5

\(\dfrac{2}{67}-\left(\dfrac{3}{7}+\dfrac{2}{67}\right)\\ =\dfrac{2}{67}-\dfrac{215}{469}\\ =\dfrac{-3}{7}\)

\(\dfrac{3}{4}.\dfrac{5}{2}+\dfrac{5}{4}.\dfrac{5}{2}\\ =\left(\dfrac{3}{4}+\dfrac{5}{4}\right).\dfrac{5}{2}\\ =2.\dfrac{5}{2}\\ =\dfrac{5}{1}\)

-472 + (235 - 28) - (35 - 350)

= -472 + 235 - 28 - 35 + 350

= (-472 - 28) + (235 - 35) + 350

= -500 + 200 + 350

= -500 + 550

= 50