Question

Rút gọn các phân thức :

a, \(\dfrac{x^{2^{ }}-4}{2x^{2^{ }}-4x}\)

b, \(\dfrac{2x-x^2}{x^2-4x+4}\)

c, \(\dfrac{x^2-xy-x+y}{x^2+xy-x-y}\)

d, \(\dfrac{5x^2+10x+5}{x+x^2}\)

e, \(\dfrac{3x^2+3x}{\left(x+1\right) \left(2x+6\right)}\)

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

Answer 1

a) \(\dfrac{x^2-4}{2x^2-4x}\)

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

\(=\dfrac{x+2}{2x}\)

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

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

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

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

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

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

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

\(=\dfrac{x-y}{x+y}\)

d) \(\dfrac{5x^2+10x+5}{x+x^2}\)

\(\dfrac{5\left(x^2+2x+1\right)}{x\left(1+x\right)}\)

\(=\dfrac{5\left(x+1\right)^2}{x\left(x+1\right)}\)

\(=\dfrac{5\left(x+1\right)}{x}\)

e) \(\dfrac{3x^2+3x}{\left(x+1\right)\left(2x+6\right)}\)

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

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

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

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

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