Toán Lớp 8: Thực hiện các phép tính sau:
a. 1-x^2/x^2-2x : x+1/x
b. 2/x+2+-4/2-x+5x+2/4-x^2
c. 1/xy-y^2-1/x^2-xy
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Toán Lớp 8: Thực hiện các phép tính sau:
a. 1-x^2/x^2-2x : x+1/x
b. 2/x+2+-4/2-x+5x+2/4-x^2
c. 1/xy-y^2-1/x^2-xy
Comments ( 1 )
a)\dfrac{{1 – {x^2}}}{{{x^2} – 2x}}:\dfrac{{x + 1}}{x}\\
= \dfrac{{\left( {1 + x} \right)\left( {1 – x} \right)}}{{x\left( {x – 2} \right)}}.\dfrac{x}{{x + 1}}\\
= \dfrac{{1 – x}}{{x – 2}}\\
b)\dfrac{2}{{x + 2}} + \dfrac{{ – 4}}{{2 – x}} + \dfrac{{5x + 2}}{{4 – {x^2}}}\\
= \dfrac{2}{{x + 2}} + \dfrac{{ – 4}}{{2 – x}} + \dfrac{{5x + 2}}{{\left( {2 – x} \right)\left( {2 + x} \right)}}\\
= \dfrac{{2\left( {2 – x} \right) – 4\left( {x + 2} \right) + 5x + 2}}{{\left( {2 – x} \right)\left( {2 + x} \right)}}\\
= \dfrac{{4 – 2x – 4x – 8 + 5x + 2}}{{\left( {2 – x} \right)\left( {2 + x} \right)}}\\
= \dfrac{{ – x – 2}}{{\left( {2 – x} \right)\left( {2 + x} \right)}}\\
= \dfrac{1}{{x – 2}}\\
c)\dfrac{1}{{xy – {y^2}}} – \dfrac{1}{{{x^2} – xy}}\\
= \dfrac{1}{{y\left( {x – y} \right)}} – \dfrac{1}{{x\left( {x – y} \right)}}\\
= \dfrac{{x – y}}{{xy\left( {x – y} \right)}}\\
= \dfrac{1}{{xy}}
\end{array}$