Question

Bài 1 : Rút gọn

\(a,\frac{12x^2y^3}{18x^3y}\)

\(b,\frac{x^2-1}{x^2+x}\)

\(c,\frac{5x^3+5x}{x^4-1}\)

\(d,\frac{2x^3+x^2-2x-1}{x^3+2x^2-x-2}\)

\(e,\frac{x^5+5x+6}{x^4+4x+4}\)

Answer 1

a) \(\frac{12x^2y^3}{18x^3y}=\frac{2y^2}{3x}\)

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

c) \(\frac{5x^3+5x}{x^4-1}=\frac{5x\left(x^2+1\right)}{\left(x^2+1\right)\left(x^2-1\right)}=\frac{5x}{x^2-1}\)

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