Question

Thực hiện các phép tính:

a)\(2x.\left(x^2+4x-3\right)\)

b)\(\left(12x^2y^3-6x^4y^2+15x^3y^3\right):\left(6x^2y^2\right)\)

c)\(\left(x-2\right).\left(4x^2+5x-3\right)\)

d)\(\dfrac{-x^2-9}{4\left(x-3\right)}+\dfrac{2x^2}{4\left(x-3\right)}\)

e)\(\dfrac{5}{x-2}+\dfrac{8x+4}{x^2-4}-\dfrac{4}{x+2}\)

f)\(\dfrac{1}{x}+\dfrac{2}{x+4}+\dfrac{-4x-8}{x^2+4x}\)

Answer 1

c) \(\left(x-2\right).\left(4x^2+5x-3\right)\)

\(=x.4x^2+x.5x+x.\left(-3\right)+\left(-2\right).4x^2+\left(-2\right).5x+\left(-2\right).\left(-3\right)\)

\(=4x^3+5x^2-3x-8x^2-10x+6\)

\(=4x^3-3x^2-13x+6\)

Answer 2

a) \(2x.\left(x^2+4x-3\right)=2x.x^2+2x.4x+2x.\left(-3\right)\)

\(=2x^3+8x^2-6x\)

Answer 3

b) \(\left(12x^2y^3-6x^4y^2+15x^3y^3\right):\left(6x^2y^2\right)\)

\(=12x^2y^3:6x^2y^2+\left(-6x^4y^2\right):6x^2y^2+15x^3y^3:6x^2y^2\)

\(=2y-x^2+\dfrac{5}{2}xy\)

Answer 4

d) ĐKXĐ: \(x\ne3\)

\(\dfrac{-x^2-9}{4\left(x-3\right)}+\dfrac{2x^2}{4\left(x-3\right)}\)

\(=\dfrac{-x^2-9+2x^2}{4\left(x-3\right)}\)

\(=\dfrac{x^2-9}{4\left(x-3\right)}\)

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

\(=\dfrac{x+3}{4}\)

Answer 5

e) ĐKXĐ: \(x\ne-2;x\ne2\)

\(\dfrac{5}{x-2}+\dfrac{8x+4}{x^2-4}-\dfrac{4}{x+2}\)

\(=\dfrac{5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{8x+4}{\left(x-2\right)\left(x+2\right)}-\dfrac{4\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{5x+10+8x+4-4x+8}{\left(x-2\right)\left(x+2\right)}\)

\(=\dfrac{9x+22}{\left(x-2\right)\left(x+2\right)}\)

Answer 6

f) ĐKXĐ: \(x\ne0;x\ne-4\)

\(\dfrac{1}{x}+\dfrac{2}{x+4}+\dfrac{-4x-8}{x^2+4x}\)

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

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

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

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

\(=\dfrac{-1}{x}\)