Bài 1:
10: ĐKXĐ: x>=0; x<>16
\(A=\dfrac{5-5\sqrt{x}}{x-16}-\dfrac{2}{4-\sqrt{x}}+\dfrac{3}{\sqrt{x}+4}\)
\(=\dfrac{-5\sqrt{x}+5+2\left(\sqrt{x}+4\right)+3\left(\sqrt{x}-4\right)}{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}\)
\(=\dfrac{-5\sqrt{x}+5+2\sqrt{x}+8+3\sqrt{x}-12}{x-16}=\dfrac{1}{x-16}\)
11: ĐKXĐ: x>=0; x<>1
\(A=\dfrac{\sqrt{x}+3}{\sqrt{x}+1}+\dfrac{5}{\sqrt[]{x}-1}+\dfrac{4}{x-1}\)
\(=\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)+5\left(\sqrt{x}+1\right)+4}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{x+2\sqrt{x}-3+5\sqrt{x}+5+4}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{x+7\sqrt{x}+6}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}=\dfrac{\sqrt{x}+6}{\sqrt{x}-1}\)
12: ĐKXĐ: x>=0; x<>4/9
\(A=\dfrac{\sqrt{x}}{2\sqrt{x}-3}+\dfrac{\sqrt{x}-2}{2\sqrt{x}+3}+\dfrac{15-4\sqrt{x}}{9-4x}\)
\(=\dfrac{\sqrt{x}\left(2\sqrt{x}+3\right)+\left(\sqrt{x}-2\right)\left(2\sqrt{x}-3\right)}{\left(2\sqrt{x}-3\right)\left(2\sqrt{x}+3\right)}+\dfrac{4\sqrt{x}-15}{\left(2\sqrt{x}-3\right)\left(2\sqrt{x}+3\right)}\)
\(=\dfrac{2x+3\sqrt{x}+2x-3\sqrt{x}-4\sqrt{x}+6+4\sqrt{x}-15}{\left(2\sqrt{x}-3\right)\left(2\sqrt{x}+3\right)}\)
\(=\dfrac{4x-9}{4x-9}=1\)
13: ĐKXĐ:\(\left\{{}\begin{matrix}x>=0\\x\ne1\end{matrix}\right.\)
\(A=\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{x-1}\right)\cdot\dfrac{4\sqrt{x}-4}{2\sqrt{x}+1}\)
\(=\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\cdot\dfrac{4\left(\sqrt{x}-1\right)}{2\sqrt{x}+1}\)
\(=\dfrac{\sqrt{x}+1+\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{4\left(\sqrt{x}-1\right)}{2\sqrt{x}+1}\)
\(=\dfrac{2\sqrt{x}+1}{\left(\sqrt{x}+1\right)}\cdot\dfrac{4}{2\sqrt{x}+1}=\dfrac{4}{\sqrt{x}+1}\)
Bài 2:
1: ĐKXĐ: x>=3
\(\sqrt{4\left(x-3\right)}+\sqrt{9x-27}=10\)
=>\(2\sqrt{x-3}+3\sqrt{x-3}=10\)
=>\(5\sqrt{x-3}=10\)
=>\(\sqrt{x-3}=2\)
=>x-3=4
=>x=7(nhận)
2:
ĐKXĐ: x>=-1
\(\sqrt{16x+16}-\sqrt{9x+9}=1\)
=>\(4\sqrt{x+1}-3\sqrt{x+1}=1\)
=>\(\sqrt{x+1}=1\)
=>x+1=1
=>x=0(nhận)
3: ĐKXĐ: x>=2
\(\sqrt{4x-8}=6-\sqrt{x-2}\)
=>\(2\sqrt{x-2}+\sqrt{x-2}=6\)
=>\(3\sqrt{x-2}=6\)
=>\(\sqrt{x-2}=2\)
=>x-2=4
=>x=6(nhận)
4: ĐKXĐ: x>=3
\(\sqrt{4x-12}=10-\sqrt{9x-27}\)
=>\(2\sqrt{x-3}=10-3\sqrt{x-3}\)
=>\(5\sqrt{x-3}=10\)
=>\(\sqrt{x-3}=2\)
=>x-3=4
=>x=7(nhận)
5: ĐKXĐ: x>=5
\(5\sqrt{x-5}+\sqrt{9x-45}=16\)
=>\(5\sqrt{x-5}+3\sqrt{x-5}=16\)
=>\(8\sqrt{x-5}=16\)
=>\(\sqrt{x-5}=2\)
=>x-5=4
=>x=4+5=9(nhận)
6: ĐKXĐ: x<=1/3
\(\sqrt{4\left(1-3x\right)}+\sqrt{9\left(1-3x\right)}=10\)
=>\(2\sqrt{1-3x}+3\sqrt{1-3x}=10\)
=>\(5\sqrt{1-3x}=10\)
=>\(\sqrt{1-3x}=2\)
=>1-3x=4
=>3x=1-4=-3
=>x=-1(nhận)
7: ĐKXĐ: x>=2
\(\sqrt{4x-8}-\dfrac{1}{3}\cdot\sqrt{9x-18}=15\)
=>\(2\sqrt[]{x-2}-\dfrac{1}{3}\cdot3\sqrt{x-2}=15\)
=>\(\sqrt{x-2}=15\)
=>\(x-2=15^2=225\)
=>x=225+2=227(nhận)
8: ĐKXĐ: x>=1
\(\sqrt{x-1}-\sqrt{4x-4}+\sqrt{9x-9}=5\)
=>\(\sqrt{x-1}-2\sqrt{x-1}+3\sqrt{x-1}=5\)
=>\(2\sqrt{x-1}=5\)
=>\(\sqrt{x-1}=\dfrac{5}{2}\)
=>\(x-1=\left(\dfrac{5}{2}\right)^2=\dfrac{25}{4}\)
=>\(x=\dfrac{25}{4}+1=\dfrac{29}{4}\left(nhận\right)\)
