Toán Lớp 8: Rút gọn các biểu thức sau:
a. A = (x/x+2+1) : (1-3x^2/4-x^2)
b. B = (2a^2/b^2-1/2) . (1/2a-b-1/2a+b)
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Toán Lớp 8: Rút gọn các biểu thức sau:
a. A = (x/x+2+1) : (1-3x^2/4-x^2)
b. B = (2a^2/b^2-1/2) . (1/2a-b-1/2a+b)
Comments ( 2 )
a)A = \left( {\dfrac{x}{{x + 2}} + 1} \right):\left( {1 – \dfrac{{3{x^2}}}{{4 – {x^2}}}} \right)\\
= \dfrac{{x + x + 2}}{{x + 2}}:\dfrac{{4 – {x^2} – 3{x^2}}}{{4 – {x^2}}}\\
= \dfrac{{2x + 2}}{{x + 2}}.\dfrac{{\left( {x – 2} \right)\left( {x + 2} \right)}}{{4\left( {{x^2} – 1} \right)}}\\
= \dfrac{{2\left( {x + 1} \right)}}{1}.\dfrac{{x – 2}}{{4.\left( {x – 1} \right)\left( {x + 1} \right)}}\\
= \dfrac{{x – 2}}{{2\left( {x – 1} \right)}}\\
= \dfrac{{x – 2}}{{2x – 2}}\\
b)B = \left( {\dfrac{{2{a^2}}}{{{b^2}}} – \dfrac{1}{2}} \right).\left( {\dfrac{1}{{2a – b}} – \dfrac{1}{{2a + b}}} \right)\\
= \dfrac{{4{a^2} – {b^2}}}{{2{b^2}}}.\dfrac{{2a + b – 2a + b}}{{{{\left( {2a} \right)}^2} – {b^2}}}\\
= \dfrac{{4{a^2} – {b^2}}}{{2{b^2}}}.\dfrac{{2b}}{{4{a^2} – {b^2}}}\\
= \dfrac{1}{b}
\end{array}$