Rút gọn biểuthức A=(a+b+1)^3-(a+b-1)^3-6(a+b)^2
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
AT
18 tháng 7 2021
mình nghĩ đề nên là \(N=\left(\dfrac{3}{\sqrt{x}+2}-\dfrac{1}{\sqrt{x}-2}\right):\left(\dfrac{\sqrt{x}-6}{x-2\sqrt{x}}+\dfrac{1}{\sqrt{x}}\right)\) chớ như bạn rút gọn không hết
\(N=\left(\dfrac{3}{\sqrt{x}+2}-\dfrac{1}{\sqrt{x}-2}\right):\left(\dfrac{\sqrt{x}-6}{x-2\sqrt{x}}+\dfrac{1}{\sqrt{x}}\right)\left(x>0,x\ne2\right)\)
\(=\dfrac{3\left(\sqrt{x}-2\right)-\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}:\left(\dfrac{\sqrt{x}-6}{\sqrt{x}\left(\sqrt{x}-2\right)}+\dfrac{1}{\sqrt{x}}\right)\)
\(=\dfrac{2\sqrt{x}-8}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}:\dfrac{\sqrt{x}-6+\sqrt{x}-2}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\dfrac{2\sqrt{x}-8}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}:\dfrac{2\sqrt{x}-8}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\dfrac{2\sqrt{x}-8}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{2\sqrt{x}-8}=\dfrac{\sqrt{x}}{\sqrt{x}+2}\)
H9
HT.Phong (9A5)
CTVHS
18 tháng 8 2023
a) \(a^{\dfrac{1}{3}}\cdot a^{\dfrac{1}{2}}\cdot a^{\dfrac{7}{6}}=a^{\dfrac{1}{3}+\dfrac{1}{2}+\dfrac{7}{6}}=a^2\)
b) \(a^{\dfrac{2}{3}}\cdot a^{\dfrac{1}{4}}:a^{\dfrac{1}{6}}=a^{\dfrac{2}{3}+\dfrac{1}{4}-\dfrac{1}{6}}=a^{\dfrac{3}{4}}\)
c) \(\left(\dfrac{3}{2}a^{-\dfrac{3}{2}}\cdot b^{-\dfrac{1}{2}}\right)\left(-\dfrac{1}{3}a^{\dfrac{1}{2}}b^{\dfrac{2}{3}}\right)=\left(\dfrac{3}{2}\cdot-\dfrac{1}{3}\right)\left(a^{-\dfrac{3}{2}}\cdot a^{\dfrac{1}{2}}\right)\left(b^{-\dfrac{1}{2}}\cdot b^{\dfrac{2}{3}}\right)\)
\(=-\dfrac{1}{2}a^{-1}b^{-\dfrac{1}{3}}\)
HL
0
NN
1
13 tháng 6 2021
a, \(B=\frac{\sqrt{a}+3}{2\sqrt{a}-6}-\frac{3-\sqrt{a}}{2\sqrt{a}+6}=\frac{\left(2\sqrt{a}+6\right)\left(\sqrt{a}+3\right)+\left(2\sqrt{a}-6\right)\left(\sqrt{a}-3\right)}{4a-36}\)
\(=\frac{2a+12\sqrt{a}+18+2a-12\sqrt{a}+18}{4a-36}=\frac{4a+36}{4a-36}=\frac{a+9}{a-9}\)
b, Ta có : \(B>1\Rightarrow\frac{a+9}{a-9}>1\Leftrightarrow\frac{a+9}{a-9}-1>0\)
\(\Leftrightarrow\frac{a+9-a+9}{a-9}>0\Leftrightarrow\frac{18}{a-9}>0\Rightarrow a-9>0\Leftrightarrow a>9\)vì 18 > 0
\(B< 1\Rightarrow\frac{a+9}{a-9}< 1\Leftrightarrow\frac{a+9}{a-9}-1< 0\)
\(\Leftrightarrow\frac{a+9-a+9}{a-9}< 0\Leftrightarrow\frac{18}{a-9}< 0\Rightarrow a-9< 0\Leftrightarrow a< 9\)vì 18 > 0
c, Ta có : \(B=4\Rightarrow\frac{a+9}{a-9}=4\Rightarrow a+9=4a-36\Leftrightarrow3a=45\Leftrightarrow a=15\)
Vậy a = 15 thì B = 4
minh nham =a2+2ab+b2