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

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

\(=\dfrac{3x+1}{\left(x-1\right)\left(x+1\right)}-\dfrac{1}{x+1}+\dfrac{-\left(x+3\right)}{\left(x+1\right)\left(x-1\right)}\)

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

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

\(=\dfrac{3x^2+4x+1-\left(x^2-2x+1\right)-\left(x^2+2x+3\right)}{\left(x-1\right)^2\left(x+1\right)}\)

\(=\dfrac{x^2+4x+3}{\left(x-1\right)^2\left(x+1\right)}\)

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

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

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

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

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

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

\(=\dfrac{3x^2+4x+1-x^2+2x-1-x^2-2x+3}{\left(x-1\right)^2\left(x+1\right)}\)

\(=\dfrac{x^2+4x+3}{\left(x-1\right)^2\left(x+1\right)}\)

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

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

\(\dfrac{18x}{x^3-9x}-\dfrac{2-x}{x+3}+\dfrac{3}{3-x}\)

=\(\dfrac{18x}{x\left(x^2-9\right)}-\dfrac{\left(2-x\right)\left(x-3\right)x}{\left(x+3\right)\left(x-3\right)x}-\dfrac{3x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)x}\)

=\(\dfrac{18x-\left(2-x\right)\left(x-3\right)x-3x\left(x+3\right)}{x\left(x+3\right)\left(x-3\right)}\)

=\(\dfrac{18x-\left(2x-6-x^2+3x\right)x-3x^2-9x}{x\left(x+3\right)\left(x-3\right)}\)

=\(\dfrac{18x-2x^2+6x+x^3-3x^2-3x^2-9x}{x\left(x+3\right)\left(x-3\right)}\)

=\(\dfrac{x^3-8x^2+15x}{x\left(x-3\right)\left(x+3\right)}\)

=\(\dfrac{x\left(x^2-8x+15\right)}{x\left(x-3\right)\left(x+3\right)}\)

=\(\dfrac{x^2-3x-5x+15}{x\left(x-3\right)\left(x+3\right)}\)

=\(\dfrac{x\left(x-3\right)-5\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

=\(\dfrac{\left(x-3\right)\left(x-5\right)}{\left(x-3\right)\left(x+3\right)}\)

=\(\dfrac{\left(x-5\right)}{x+3}\)

BẠN CŨNG CHƠI MINECRAFT AK

Chúc bạn học tốt!

B = ( \(\dfrac{5}{7}.0,6:3\dfrac{1}{2}\)) . ( 40% - 1,4) . \(\left(-2\right)^3\)

= (\(\dfrac{5}{7}.\dfrac{3}{5}\): \(\dfrac{7}{2}\)) . ( \(\dfrac{2}{5}-\dfrac{7}{5}\)) . (-8)

= (\(\dfrac{15}{35}:\dfrac{7}{2}\)) . \(\dfrac{-5}{5}\) . ( -8)

= (\(\dfrac{3}{7}.\dfrac{2}{7}\)) . (-1) . (-8)

= \(\dfrac{6}{49}\) . (-1) . (-8)

= \(\dfrac{-6}{49}\) . (-8)

= \(\dfrac{48}{49}\)

Vậy: B =\(\dfrac{48}{49}\)

Nhớ tick nha

B=(\(\dfrac{3}{7}.\dfrac{2}{7}\)).(\(\dfrac{4}{10}-\dfrac{14}{10}\)).(-8)

B=\(\dfrac{3}{7}.\left(-1\right)\left(-8\right)\)

B=\(\dfrac{24}{7}\)

2xyz+4xyz-\(\frac{1}{2}\) xyz

=(2+4-\(\frac{1}{2}\) )(xxxyyyzzz)

=3.5x³ y³z³

\(a,=\dfrac{\left(x-2\right)^2-\left(x+2\right)^2}{\left(x-2\right)^2\left(x+2\right)^2}:\dfrac{x-2+x+2}{\left(x-2\right)\left(x+2\right)}\\ =\dfrac{-8x}{\left(x-2\right)^2\left(x+2\right)^2}\cdot\dfrac{\left(x-2\right)\left(x+2\right)}{2x}=\dfrac{-4}{\left(x-2\right)\left(x+2\right)}\)

\(b,=\dfrac{5x^2+26xy+5y^2+5x^2-26xy+5y^2}{x\left(x-5y\right)\left(x+5y\right)}\cdot\dfrac{\left(x-5y\right)\left(x+5y\right)}{x^2+y^2}\\ =\dfrac{10\left(x^2+y^2\right)}{x\left(x^2+y^2\right)}=\dfrac{10}{x}\)

Giải:

a) \(1\dfrac{1}{2}.2\dfrac{1}{3}+1\dfrac{1}{3}.\dfrac{1}{2}\)

\(=\dfrac{3}{2}.\dfrac{7}{3}+\dfrac{4}{3}.\dfrac{1}{2}\)

\(=\dfrac{21}{6}+\dfrac{4}{6}\)

\(=\dfrac{1}{6}\left(21+4\right)\)

\(=\dfrac{25}{6}\)

b) \(\dfrac{1}{9}.\dfrac{2}{145}-4\dfrac{1}{3}.2\dfrac{2}{145}+\dfrac{2}{145}\)

\(=\dfrac{1}{9}.\dfrac{2}{145}-\dfrac{13}{3}.\dfrac{292}{145}+\dfrac{2}{145}\)

\(=\dfrac{2}{145}\left(\dfrac{1}{9}-\dfrac{13}{3}.146+1\right)\)

\(=\dfrac{2}{145}\left(-\dfrac{5684}{9}\right)\)

\(=-\dfrac{392}{45}\)

Vậy ...

a: \(=\left(1+\dfrac{4}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{16}{21}\right)+\dfrac{1}{2}\)

\(=1+1+\dfrac{1}{2}=2+\dfrac{1}{2}=\dfrac{5}{2}\)

b: \(=\left(\dfrac{1}{25}+\dfrac{5}{25}+\dfrac{25}{25}\right):\left(\dfrac{1}{25}-\dfrac{5}{25}-\dfrac{25}{25}\right)\)

\(=\dfrac{31}{25}:\dfrac{-29}{25}=\dfrac{-31}{29}\)

c: \(=\dfrac{\dfrac{1}{9}-\dfrac{1}{7}-\dfrac{1}{11}}{\dfrac{4}{9}-\dfrac{4}{7}-\dfrac{4}{11}}+\dfrac{\dfrac{3}{5}-\dfrac{3}{25}-\dfrac{3}{125}-\dfrac{3}{625}}{\dfrac{4}{5}-\dfrac{4}{25}-\dfrac{4}{125}-\dfrac{4}{625}}\)

=1/4+3/4

=1

Giải:

a) \(1\dfrac{1}{2}.2\dfrac{1}{3}+1\dfrac{1}{3}.\dfrac{1}{2}\)

\(=\dfrac{3}{2}.\dfrac{7}{3}+\dfrac{4}{3}.\dfrac{1}{2}\)

\(=\dfrac{21}{6}+\dfrac{4}{6}\)

\(=\dfrac{1}{6}\left(21+4\right)\)

\(=\dfrac{1}{6}.25=\dfrac{25}{6}\)

b) \(\dfrac{1}{9}.\dfrac{2}{145}-4\dfrac{1}{3}.\dfrac{2}{145}+\dfrac{2}{145}\)

\(=\dfrac{1}{9}.\dfrac{2}{145}-\dfrac{13}{3}.\dfrac{2}{145}+\dfrac{2}{145}\)

\(=\dfrac{2}{145}\left(\dfrac{1}{9}-\dfrac{13}{3}+1\right)\)

\(=\dfrac{2}{145}\left(-\dfrac{29}{9}\right)\)

\(=-\dfrac{2}{45}\)

Vậy ...