\(=\left[\dfrac{a^6b^3}{c^3d^6}\cdot\dfrac{ac^4}{b^2d^3}\right]:\left[\dfrac{a^8b^8}{c^4d^{12}}\cdot\dfrac{c^3}{b^9d^3}\right]\)
\(=\dfrac{a^7b^3c^4}{c^3d^9b^2}:\dfrac{a^8}{bcd^{15}}\)
\(=\dfrac{a^7bc}{d^9}\cdot\dfrac{bcd^{15}}{a^8}=\dfrac{d^6\cdot b^2\cdot c^2}{a}\)
Cho P = \(\left(\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{\sqrt{x}}{x-1}\right):\left(\frac{2}{x}-\frac{2-x}{x\left(\sqrt{x}+1\right)}\right)\)
a) Rút gọn P
b) Tính P với x=\(\frac{2}{2-\sqrt{3}}\)
c) Tìm giá trị nhỏ nhất của \(\sqrt{P}\)
Cho a,b,c >0 thỏa mãn a+b+c=1 .Tính P=\(\sqrt{\frac{\left(a+bc\right)\left(b+ca\right)}{c+ab}}+\sqrt{\frac{\left(b+ca\right)\left(c+ab\right)}{a+bc}}+\sqrt{\frac{\left(c+ab\right)\left(a+bc\right)}{b+ac}}\)
Ai giúp với
Đề bài: Rút gọn biểu thức:
1. \(\frac{\sqrt{a^2+x^2}+\sqrt{a^2-x^2}}{\sqrt{a^2+x^2}-\sqrt{a^2-x^2}}-\sqrt{^{ }\frac{a^4}{x^4}-1}\)
2. \(\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\) . \(\left(\frac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)\)
3. \(\left(\frac{3}{\sqrt{1+x}}\sqrt{1-x}\right)\) : \(\left(\frac{3}{\sqrt{1-x^2}}+1\right)\)
4. \(\left(\sqrt{a}+\frac{b-\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\right)\) : \(\left(\frac{a}{\sqrt{ab+b}}+\frac{b}{\sqrt{ab}-a}-\frac{a+b}{\sqrt{ab}}\right)\)
5. \(\frac{\sqrt{a}+\sqrt{b}-1}{a+\sqrt{ab}}\) + \(\frac{\sqrt{a}-\sqrt{b}}{2\sqrt{ab}}\) .\(\left(\frac{\sqrt{b}}{a-\sqrt{ab}}+\frac{\sqrt{b}}{a+\sqrt{ab}}\right)\)
Các bạn giúp tớ nhé, hứa sẽ tick, tớ cảm ơn!!!!
\(P=\left(2+\frac{a+\sqrt{a}}{\sqrt{a}+1}\right)\left(2-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\) (a ≥ 0 ; a ≠1)
a, Rút gọn biểu thức P.
b, Tìm giá trị lớn nhất của P.
C1. Tính:
a) \(\left(3\sqrt{\frac{3}{5}}-\sqrt{\frac{5}{3}}+\sqrt{5}\right)2\sqrt{5}+\frac{2}{3}\sqrt{75}\)
b) \(\left(\sqrt{3}-1\right)^2-\sqrt{\left(1-\sqrt{3}\right)^2}+\sqrt{\left(-3\right)^2.3}\)
C2. Tính
P = \(\frac{a-b}{\sqrt{a}+\sqrt{b}}+\frac{a\sqrt{a}-b\sqrt{b}}{a+b+\sqrt{ab}}\) , \(a\ge0,b\ge0,a\ne b\)
cho biểu thức P=\(\left[\frac{a+3\sqrt{a}+2}{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}\right]:\left(\frac{1}{\sqrt{a}+1}+\frac{1}{\sqrt{a}-1}\right)\)
a/ Rút gọn P
b/ Tìm a để \(\frac{1}{P}-\frac{\sqrt{a}+1}{8}\ge1\)
Cho biểu thức P=\(\left[\frac{a+3\sqrt{a}+2}{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}\right]:\left(\frac{1}{\sqrt{a}+1}+\frac{1}{\sqrt{a}-1}\right)\)
a/ Rút gọn P
b/ Tìm a để \(\frac{1}{P}-\frac{\sqrt{a}+1}{8}\ge1\)
rút gọn A = \(\frac{\sqrt{a}\left(1-a\right)^2}{1+a}:\left[\left(\frac{1-\sqrt{a^3}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\frac{1+\sqrt{a^3}}{1+\sqrt{a}}-\sqrt{a}\right)\right]\)
A) \(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)
b) \(\left(\frac{\sqrt{7}-\sqrt{14}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}+\sqrt{5}}\)
c) \(\left(\sqrt{3}+1\right)\sqrt{4-2\sqrt{3}}\)
d) \(5\sqrt{2}+\sqrt{18}-\sqrt{98}-\sqrt{288}\)
e)\(\left(\frac{\sqrt{3}-\sqrt{6}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{3}+\sqrt{5}}\)
g)\(\left(\sqrt{3}-1\right)\sqrt{4+2\sqrt{3}}\)
