đk: \(x\ge0,x\ne1\)
\(=>A=\left[1+\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+1}\right]\left[1-\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\right]\)
\(=\left(1+\sqrt{x}\right)\left(1-\sqrt{x}\right)=1-x\)
. đk: \(a>0,a\ne1\)
\(=>B=\left[\dfrac{\sqrt{a}+2}{\left(\sqrt{a}+1\right)^2}-\dfrac{\sqrt{a}-2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right].\dfrac{\sqrt{a}+1}{\sqrt{a}}\)
\(=\left[\dfrac{a+\sqrt{a}-2-a+\sqrt{a}+2}{\left(\sqrt{a}+1\right)^2\left(\sqrt{a}-1\right)}\right].\dfrac{\sqrt{a}+1}{\sqrt{a}}\)
\(=\left[\dfrac{2\sqrt{a}}{\left(\sqrt{a}+1\right)^2\left(\sqrt{a}-1\right)}\right].\dfrac{\sqrt{a}+1}{\sqrt{a}}=\dfrac{2}{a-1}\)
,đk: \(a>0,a\ne1\)
\(=>C=\left[\dfrac{1+\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\right].\dfrac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}=\dfrac{\sqrt{a}-1}{\sqrt{a}}\)
\(A=\left(1+\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\right)\left(1-\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\right)=\left(1+\sqrt{x}\right)\left(1-\sqrt{x}\right)=1-x\left(x\ge0;x\ne1\right)\)
\(B=\left(\dfrac{\sqrt{a}+2}{a+2\sqrt{a}+1}-\dfrac{\sqrt{a}-2}{a-1}\right)\cdot\dfrac{\sqrt{a}+1}{\sqrt{a}}=\left[\dfrac{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)-\left(\sqrt{a}-2\right)\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+1\right)^2\left(\sqrt{a}-1\right)}\right]\cdot\dfrac{\sqrt{a}+1}{\sqrt{a}}=\dfrac{\left(a+\sqrt{a}-2-a+\sqrt{a}+2\right)}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)\sqrt{a}}=\dfrac{2}{a-1}\)
\(a\ge0;a\ne1\)
\(C=\left(\dfrac{1}{a-\sqrt{a}}+\dfrac{1}{\sqrt{a}-1}\right):\dfrac{\sqrt{a}+1}{a-2\sqrt{a}+1}=\dfrac{1+\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\dfrac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}=\dfrac{\sqrt{a}-1}{\sqrt{a}}\\ a \ge0;a\ne1\)
B=(√a+2a+2√a+1−√a−2a−1)⋅√a+1√a=⎡⎣(√a+2)(√a−1)−(√a−2)(√a+1)(√a+1)2(√a−1)⎤⎦⋅√a+1√a=(a+√a−2−a+√a+2)(√a+1)(√a−1)√a=2a−1B=(a+2a+2a+1−a−2a−1)⋅a+1a=[(a+2)(a−1)−(a−2)(a+1)(a+1)2(a−1)]⋅a+1a=(a+a−2−a+a+2)(a+1)(a−1)a=2a−1
a≥0;a≠1a≥0;a≠1
HT
a) Ta có: \(A=\left(1+\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\right)\left(1-\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\right)\)
\(=\left(1+\sqrt{x}\right)\left(1-\sqrt{x}\right)\)
=1-x
Ai giúp em với ạ em cần rất gấp bài 4 thôi ạ
em cần giải gấp bài 2 ạ, mọi người giúp em với ạ
giúp em với ạ, cần gấp ạ TvT