Toán Lớp 8: Thực hiện phép tính rút gọn các biểu thức sau
a) 5/x + x/x+6 – 30/x²+6x
b) 2-4x/ x²-1 + 2/x+1 – x/1-x
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Toán Lớp 8: Thực hiện phép tính rút gọn các biểu thức sau
a) 5/x + x/x+6 – 30/x²+6x
b) 2-4x/ x²-1 + 2/x+1 – x/1-x
Comments ( 1 )
a)\dfrac{5}{x} + \dfrac{x}{{x + 6}} – \dfrac{{30}}{{{x^2} + 6x}}\\
= \dfrac{5}{x} + \dfrac{x}{{x + 6}} – \dfrac{{30}}{{x\left( {x + 6} \right)}}\\
= \dfrac{{5\left( {x + 6} \right) + x.x – 30}}{{x\left( {x + 6} \right)}}\\
= \dfrac{{{x^2} + 5x}}{{x\left( {x + 6} \right)}}\\
= \dfrac{{x\left( {x + 5} \right)}}{{x\left( {x + 6} \right)}}\\
= \dfrac{{x + 5}}{{x + 6}}\\
b)\dfrac{{2 – 4x}}{{{x^2} – 1}} + \dfrac{2}{{x + 1}} – \dfrac{x}{{1 – x}}\\
= \dfrac{{2 – 4x + 2\left( {x – 1} \right) + x\left( {x + 1} \right)}}{{\left( {x + 1} \right)\left( {x – 1} \right)}}\\
= \dfrac{{2 – 4x + 2x – 2 + {x^2} + x}}{{\left( {x + 1} \right)\left( {x – 1} \right)}}\\
= \dfrac{{{x^2} – x}}{{\left( {x + 1} \right)\left( {x – 1} \right)}}\\
= \dfrac{{x\left( {x – 1} \right)}}{{\left( {x + 1} \right)\left( {x – 1} \right)}}\\
= \dfrac{x}{{x + 1}}
\end{array}$