Em cần kiểm tra đáp án bài nào nhỉ?
1.
a.
\(P=\dfrac{x^2}{x^2-4}+\dfrac{1}{x+2}+\dfrac{1}{x-2}=\dfrac{x^2}{\left(x-2\right)\left(x+2\right)}+\dfrac{x-2}{\left(x-2\right)\left(x+2\right)}+\dfrac{x+2}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2+x-2+x+2}{\left(x-2\right)\left(x+2\right)}=\dfrac{x^2+2x}{\left(x-2\right)\left(x+2\right)}=\dfrac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x}{x-2}\)
b.
\(P=\dfrac{x}{x-2}=\dfrac{x-2+2}{x-2}=1+\dfrac{2}{x-2}\)
Để P nguyên \(\Rightarrow\dfrac{2}{x-2}\) nguyên
\(\Rightarrow x-2=Ư\left(2\right)\)
\(\Rightarrow x-2=\left\{-2;-1;1;2\right\}\)
\(\Rightarrow x=\left\{0;1;3;4\right\}\)
2.
a.
Căn thức đã cho có nghĩa khi:
\(3x-2\ge0\Leftrightarrow3x\ge2\Rightarrow x\ge\dfrac{2}{3}\)
b.
\(A=2\sqrt{9}+3\sqrt{49}-\sqrt{64}=2\sqrt{3^2}+3\sqrt{7^2}-\sqrt{8^2}\)
\(=2.3+3.7-8=19\)
c.
\(\sqrt{\left(\sqrt{3}-1\right)^2}=\left|\sqrt{3}-1\right|=\sqrt{3}-1\) (do \(\sqrt{3}-1>0\))
d.
\(2\left(x+3\right)+5x-6=3\left(2x-1\right)\)
\(\Leftrightarrow2x+6+5x-6=6x-3\)
\(\Leftrightarrow7x=6x-3\)
\(\Leftrightarrow x=-3\)
