Question

giúp em vs mn

Answer 1

a: \(=4ax^2y:\dfrac{1}{2}x^2y-\dfrac{1}{3}x^3y:\dfrac{1}{2}x^2y+\dfrac{2}{3}x^4y^3:\dfrac{1}{2}x^2y\)

\(=8a-\dfrac{2}{3}x+\dfrac{4}{3}x^2y^2\)

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

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

\(=2x^2+3x-2\)

c: \(=\dfrac{x^2-3x+3x-16}{x-4}=\dfrac{x^2-16}{x-4}=x+4\)

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

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

e: \(=\dfrac{2}{x+2}-\dfrac{8}{\left(x+2\right)\left(x-2\right)}+\dfrac{2}{x-2}\)

\(=\dfrac{2x-4-8+2x+4}{\left(x-2\right)\left(x+2\right)}=\dfrac{4x-8}{\left(x-2\right)\left(x+2\right)}=\dfrac{4}{x+2}\)

f: \(=\dfrac{3x+2-3x+2+3x-6}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{3x-2}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{1}{3x+2}\)

g: \(=\dfrac{3}{\left(x+y\right)^2}+\dfrac{5}{\left(x-y\right)\left(x+y\right)}-\dfrac{4}{\left(x-y\right)^2}\)

\(=\dfrac{3x^2-6xy+3y^2+5x^2-5y^2-4x^2-8xy-4y^2}{\left(x-y\right)^2\cdot\left(x+y\right)^2}\)

\(=\dfrac{4x^2-14xy-6y^2}{\left(x-y\right)^2\cdot\left(x+y\right)^2}\)

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

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

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

i: \(=\dfrac{3x+2}{\left(x-1\right)^2}-\dfrac{6}{\left(x-1\right)\left(x+1\right)}+\dfrac{2-3x}{\left(x+1\right)^2}\)

\(=\dfrac{\left(3x+2\right)\left(x+1\right)^2-6\left(x^2-1\right)+\left(2-3x\right)\left(x-1\right)^2}{\left(x-1\right)^2\cdot\left(x+1\right)^2}\)

\(=\dfrac{3x^3+8x^2+7x+2-6x^2+6-3x^3+8x^2-7x+2}{\left(x-1\right)^2\cdot\left(x+1\right)^2}\)

\(=\dfrac{10x^2+10}{\left(x-1\right)^2\cdot\left(x+1\right)^2}\)