Bài 100611

Question

Rút gọn biểu thức
\(
C=[\left (\frac{a+1}{a-1} \right )^{2}+3]\div [ \left ( \frac{a-1}{a+1} \right )^{2}+3 ] \div \frac{a^{3}+1}{a^{3}-1} - \frac{2a}{a-1}
\)

score 0 · Answer 1

\(
C=\frac{\left ( a+1 \right )^{2}+3\left ( a-1 \right )^{2}}{\left ( a-1 \right )^{2}} \div \frac{\left ( a-1 \right )^{2} + 3\left ( a+1 \right )^{2}}{\left (a+1 \right )^{2}} \div \frac{a^{3} +1}{a^{3} -1} - \frac{2a}{a-1}
\)

\(
=\frac{a^{2}+2a+1+3a^{2}-6a+3}{\left ( a-1 \right )^{2}} \times \frac{\left ( a+1 \right )^{2}}{a^{2}-2a+1+3a^{2}+6a+3} \times \frac{\left ( a-1 \right )\left ( a^{2}+a+1 \right )}{\left ( a+1 \right )\left ( a^{2}-a+1\right )} - \frac{2a}{a-1}
\)

\(
=\frac{4\left ( a^{2}-a+1 \right )}{\left ( a-1 \right )^{2}}\times \frac{\left ( a+1 \right )^{2}}{4\left ( a^{2}+a+1 \right )} \times \frac{\left ( a-1 \right )}{\left ( a+1 \right )} \times \frac{\left ( a^{2}+a+1 \right )}{\left ( a^{2}-a+1\right )} - \frac{2a}{a-1}
\)

\(
=\frac{a+1}{a-1}-\frac{2a}{a-1} = \frac{1-a}{a-1} = -1
\)

Bài 100611

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Bài 100611

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