Cho biểu thức P= ( 1+ căn a/ a+1): ( 1/ căn a-1- 2 căn 1/ acăn a + căn a- a-1 . a) Rút gọn P.
Cho biểu thức P=(1+√aa+1):(1√a−1−2√aa√a+√a−a−1) .
a) Rút gọn P.
P=(1+√aa+1):(1√a−1−2√aa√a+√a−a−1)
=(1+√aa+1):(1√a−1−2√a(a+1)(√a−1))
ĐKXĐ: a ≥ 0; a ≠ −1; a ≠ 1.
Ta có: P=(1+√aa+1):(1√a−1−2√a(a+1)(√a−1))=a+√a+1a+1:(a+1(a+1)(√a−1)−2√a(a+1)(√a−1))
=a+√a+1a+1:a−2√a+1(a+1)(√a−1)
=a+√a+1a+1:(√a−1)2(a+1)(√a−1)
=a+√a+1a+1:√a−1a+1
=(a+√a+1)(a+1)(a+1)(√a−1)
=a+√a+1√a−1