Question

1. Thực hiện phép tính:

a.\(\dfrac{x}{x-3}\)+ \(\dfrac{9-6x}{x^{2^{ }}-3x}\)

b. \(\dfrac{6x^2}{6x-1}\)- \(\dfrac{x}{6x-1}\)

c. \(\dfrac{2}{x-y}\)+\(\dfrac{3}{x+y}\)+\(\dfrac{4x}{y^{2^{ }}-x^2}\)

d. \(\dfrac{x+1}{x^{2^{ }}-2x+1}\): \(\dfrac{x+1}{5x-5}\)

e. \(\dfrac{7x+6}{2x\left(x+7\right)}\) - \(\dfrac{3x+6}{2x^2+14x}\)

f. \(\dfrac{3x+21}{x^2-9}\)+\(\dfrac{2}{x+3}\)+\(\dfrac{3}{3-x}\)

g. (\(\dfrac{x}{x^2-36}\) - \(\dfrac{x-6}{x^{2^{ }}+6x}\)) : \(\dfrac{2x-6}{x^2+6x}\) + \(\dfrac{x}{6-x}\)

Answer 1

a) \(\dfrac{x}{x-3}+\dfrac{9-6x}{x^2-3x}=\dfrac{x^2}{x\left(x-3\right)}+\dfrac{9-6x}{x\left(x-3\right)}=\dfrac{x^2-6x+9}{x\left(x-3\right)}=\dfrac{\left(x-3\right)^2}{x\left(x-3\right)}=\dfrac{x-3}{x}\)

Answer 2

b: \(=\dfrac{6x^2-x}{6x-1}=x\)

c: \(=\dfrac{2x+2y+3x-3y-4x}{\left(x-y\right)\left(x+y\right)}=\dfrac{x-y}{\left(x-y\right)\left(x+y\right)}=\dfrac{1}{x+y}\)

d: \(=\dfrac{x+1}{\left(x-1\right)^2}\cdot\dfrac{5\left(x-1\right)}{x+1}=\dfrac{5}{x-1}\)

f: \(=\dfrac{3x+21+2x-6-3x-9}{\left(x-3\right)\left(x+3\right)}=\dfrac{2x+6}{\left(x-3\right)\left(x+3\right)}=\dfrac{2}{x-3}\)