Rút gọn biểu thức\(\frac{X\sqrt{X}-2\sqrt{X}+28}{X-3\sqrt{X}-4}-\frac{\sqrt{X}-4}{\sqrt{X}+1}+\frac{\sqrt{X}+8}{4-\sqrt{X}}\)
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30 tháng 7 2018
=\(\frac{x\sqrt{x}-2x+28}{x-3\sqrt{x}-4}\)- \(\frac{\sqrt{x}-4}{\sqrt{x}+1}\)- \(\frac{\sqrt{x}+8}{\sqrt{x}-4}\)
= \(\frac{x\sqrt{x}-2x+28-\left(x-16\right)-\left(\sqrt{x}+1\right)\left(\sqrt{x}+8\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
=\(\frac{x\sqrt{x}-2x+28-x+16-\left(x+9\sqrt{x}+8\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
=\(\frac{x\sqrt{x}-3x+44-x-9\sqrt{x}-8}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
=\(\frac{x\sqrt{x}-9\sqrt{x}-4x+36}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
=\(\frac{\sqrt{x}\left(x-9\right)-4\left(x-9\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)= \(\frac{\left(\sqrt{x}-4\right)\left(x-9\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
=\(\frac{x-9}{\sqrt{x}+1}\)
LT
2
YY
5 tháng 7 2018
\(\frac{\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}}{\frac{16}{\frac{16}{x^2}-\frac{8}{x}+1}}\)\(=\frac{\sqrt{x-4+4\sqrt{x-4}+4}+\sqrt{x-4-4\sqrt{x-4}+4}}{\left(\frac{4}{x}-1\right)^2}\)
\(\frac{\sqrt{\left(\sqrt{x-4}+2\right)^2}+\sqrt{\left(\sqrt{x-4}-2\right)^2}}{\left(\frac{4}{x}-1\right)^2}\)\(=\frac{\sqrt{x-4}+2+\sqrt{x-4}-2}{\left(\frac{4-x}{x}\right)^2}\)
\(=\frac{2\sqrt{x-4}}{\left(\frac{4-x}{x}\right)^2}=\frac{2x^2\sqrt{x-4}}{\left(x-4\right)^2}=\frac{2x^2}{\sqrt{x-4}^3}\)
KT
5 tháng 7 2018
bài bạn YIM YIM sai nhé, mk làm lại và chỉnh lại đề luôn, bạn tham khảo:
ĐK: \(x>4\)
\(A=\frac{\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}}{\frac{16}{x^2}-\frac{8}{x}+1}\)
\(=\frac{\sqrt{\left(\sqrt{x-4}+2\right)^2}+\sqrt{\left(\sqrt{x-4}-2\right)^2}}{\left(1-\frac{4}{x}\right)^2}\)
\(=\frac{\sqrt{x-4}+2+\left|\sqrt{x-4}-2\right|}{\left(\frac{x-4}{x}\right)^2}\)
Nếu \(4< x\le8\)thì:
\(A=\frac{\sqrt{x-4}+2+2-\sqrt{x-4}}{\left(\frac{x-4}{x}\right)^2}\)
\(=\frac{4x^2}{\left(x-4\right)^2}\)
Nếu \(x>8\)thì:
\(A=\frac{\sqrt{x-4}+2+\sqrt{x-4}-2}{\frac{\left(x-4\right)^2}{x^2}}=\frac{2x^2}{\sqrt{x-4}^3}\)
đk: \(x\ge0;x\ne16\)
\(\frac{x\sqrt{x}-2\sqrt{x}+28}{x-3\sqrt{x}-4}-\frac{\sqrt{x}-4}{\sqrt{x}+1}-\frac{\sqrt{x}+8}{\sqrt{x}-4}\)
\(=\frac{x\sqrt{x}-2\sqrt{x}+28-\left(\sqrt{x}-4\right)^2-\left(\sqrt{x}+8\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
\(=\frac{x\sqrt{x}-2\sqrt{x}+28-x+8\sqrt{x}-16-x-9\sqrt{x}-8}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
\(=\frac{x\sqrt{x}-2x-3\sqrt{x}+4}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
\(=\frac{\left(x\sqrt{x}-x\right)-\left(x-\sqrt{x}\right)-\left(4\sqrt{x}-4\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
\(=\frac{\left(\sqrt{x}-1\right)\left(x-\sqrt{x}-4\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
:vvv