Question

Thực hiện các phép tính sau:

a) \(\dfrac{{{x^2} - 9}}{{x - 2}}:\dfrac{{x - 3}}{x}\)                        b) \(\dfrac{x}{{{z^2}}} \cdot \dfrac{{xz}}{{{y^3}}}:\dfrac{{{x^3}}}{{yz}}\)                    c) \(\dfrac{2}{x} - \dfrac{2}{x}:\dfrac{1}{x} + \dfrac{4}{x} \cdot \dfrac{{{x^2}}}{2}\)   

Answer 1

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

\(b,\dfrac{x}{z^2}.\dfrac{xz}{y^3}:\dfrac{x^3}{yz}\\ =\dfrac{x}{z^2}.\dfrac{xz}{y^3}.\dfrac{yz}{x^3}=\dfrac{x^2yz^2}{z^2y^3x^3}=\dfrac{1}{xy^2}\)

\(c,\dfrac{2}{x}-\dfrac{2}{x}:\dfrac{1}{x}+\dfrac{4}{x}.\dfrac{x^2}{2}\\ =\dfrac{2}{x}-\dfrac{2}{x}\times\dfrac{x}{1}+\dfrac{4x^2}{2x}\\ =\dfrac{2}{x}-\dfrac{2}{1}+2x\\ =\dfrac{2-2x+2x^2}{x}\)

Answer 2

a) \(\dfrac{x^2-9}{x-2}:\dfrac{x-3}{x}\)

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

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

b) \(\dfrac{x}{z^2}\cdot\dfrac{xz}{y^3}:\dfrac{x^3}{yz}\)

\(=\dfrac{x}{z^2}\cdot\dfrac{xz}{y^3}\cdot\dfrac{yz}{x^3}\)

\(=\dfrac{1}{xy^2}\)

c) \(\dfrac{2}{x}-\dfrac{2}{x}:\dfrac{1}{x}+\dfrac{4}{x}\cdot\dfrac{x^2}{2}\)

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

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

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

\(=\dfrac{6}{x}-2\)