b: \(B=\dfrac{3y+5}{y-1}-\dfrac{-y^2-4y}{y-1}+\dfrac{y^2+y+7}{y-1}\)

\(=\dfrac{3y+5+y^2+4y+y^2+y+7}{y-1}\)

\(=\dfrac{2y^2+8y+12}{y-1}\)

Bài 1: 

a, (\(x\) - 4).(\(x\) + 4) - (5 - \(x\)).(\(x\) + 1)

= \(x^2\) -  16 - 5\(x\) - 5 + \(x^2\) + \(x\) 

= (\(x^2\) + \(x^2\)) - (5\(x\) - \(x\)) - (16 + 5)

= 2\(x^2\) - 4\(x\) - 21

b, (3\(x^2\) - 2\(xy\) + 4) + (5\(xy\) - 6\(x^2\) - 7)

=  3\(x^2\) - 2\(xy\) + 4 + 5\(xy\) - 6\(x^2\) - 7

= (3\(x^2\) - 6\(x^2\)) + (5\(xy\) - 2\(xy\)) - (7 - 4)

= - 3\(x^2\) + 3\(xy\) - 3

a: \(N=\dfrac{3x^5-4x^4+6x^3}{-2x^2}=-\dfrac{3}{2}x^3+2x^2-3x\)

b: \(N=\dfrac{\left(6x^4y^5-3x^3y^4+\dfrac{1}{2}x^4y^3z\right)}{-\dfrac{1}{3}x^2y^3}=-18x^2y^2+9xy-\dfrac{3}{2}x^2z\)

c: \(\Leftrightarrow N\cdot\left(y-x\right)=\left(x-y\right)^3\)

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

d: \(\Leftrightarrow N\cdot\left(y^2-x^2\right)=\left(y^2-x^2\right)^2\)

hay \(N=y^2-x^2\)

a) \(3y^2\left(2y-1\right)+y-y\left(1-y+y^2\right)-y^2+y \)

= \(6y^3-3y^2+y-y+y^2-y^3-y^2+y\)

= \(5y^3-3y^2+y\)

b)\(25x-4\left(3x-1\right)+\left(5-2x\right)7\)

= \(25x-12x+4+35-14x\)

= \(-x+39\)

c) \(11x-2\left(10x-1\right)-\left(4x-1\right)\left(-2\right)\)

= \(11x-\left(20x-2\right)-\left(-8x+2\right)\)

= \(11x-20x+2+8x-2\)

= \(-x\)

d) \(\left(\frac{1}{2x}\right)3-x\left(1-2x-\frac{1}{8x^2}\right)-x\left(x+\frac{1}{2}\right)\)

= \(\frac{3}{2x}-x+2x^2+\frac{x}{8x^2}-x^2-\frac{x}{2}\)

= \(\left(\frac{3}{2x}+\frac{1}{8x}-\frac{x}{2}\right)+x^2-x\)

= \(\left(\frac{12+1-4x^2}{8x}\right)+x^2-x\)

= \(\frac{13-4x^2}{8x}+\frac{8x^3}{8x}-\frac{8x^2}{8x}\)

= \(\frac{13-4x^2+8x^3-8x^2}{8x}\)

= \(\frac{8x^3-12x^2+13}{8x}\)

= x² - \(\frac{3}{2}\)+\(\frac{13}{8x}\)

e) \(12\left(2-3x\right)+35x-\left(x+1\right)\left(-5\right)\)

= \(24-36x+35x-\left(-5x-5\right)\)

= \(24-36x+35x+5x+5\)

= 4x + 29

câu d:(-1/2x)3-x.(1-2x-1/8x2)-x.(x+1/2) nha

a: \(x^2+x-2x-2\)

\(=x\left(x+1\right)-2\left(x+1\right)\)

\(=\left(x+1\right)\left(x-2\right)=\left(-1+1\right)\left(-1-2\right)=0\)

b: \(3x^2-2x+9x-6\)

\(=x\left(3x-2\right)+3\left(3x-2\right)\)

\(=\left(3x-2\right)\left(x+3\right)=\left(3\cdot7-2\right)\left(7+3\right)\)

\(=19\cdot10=190\)

c: \(2x^2-3xy-xy^2\)

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

\(=2\left(2\cdot2-3\cdot3-9\right)\)

\(=2\cdot\left(4-18\right)=-28\)