giúp mình câu b, c với ạ. mình đang cần gấp í :<
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a: Ta có: \(\frac{\sqrt{x}+1}{2\sqrt{x}-2}-\frac{\sqrt{x}-1}{2\sqrt{x}+2}-\frac{x+1}{1-x}\)
\(=\frac{\sqrt{x}+1}{2\left(\sqrt{x}-1\right)}-\frac{\sqrt{x}-1}{2\left(\sqrt{x}+1\right)}+\frac{x+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{\left(\sqrt{x}+1\right)^2-\left(\sqrt{x}-1\right)^2+2\left(x+1\right)}{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{x+2\sqrt{x}+1-x+2\sqrt{x}-1+2x+2}{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{2x+4\sqrt{x}+2}{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{x+2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{\left(\sqrt{x}+1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(A=\left(\frac{\sqrt{x}+1}{2\sqrt{x}-2}-\frac{\sqrt{x}-1}{2\sqrt{x}+2}-\frac{x+1}{1-x}\right)\cdot\frac{x+2\sqrt{x}+1}{x+\sqrt{x}}\)
\(=\frac{\sqrt{x}+1}{\sqrt{x}-1}\cdot\frac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}\left(\sqrt{x}+1\right)}=\frac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}\left(\sqrt{x}-1\right)}\)
b: Thay \(x=7-2\sqrt6=\left(\sqrt6-1\right)^2\) vào A, ta được:
\(A=\frac{\left(\sqrt{\left(\sqrt6-1\right)^2}+1\right)^2}{\sqrt{\left(\sqrt6-1\right)^2}\cdot\left(\sqrt{\left(\sqrt6-1\right)^2}-1\right)}\)
\(=\frac{\left(\sqrt6-1+1\right)^2}{\left(\sqrt6-1\right)\left(\sqrt6-1-1\right)}=\frac{6}{\left(\sqrt6-1\right)\left(\sqrt6-2\right)}=\frac{6}{6-3\sqrt6+2}=\frac{6}{8-3\sqrt6}\)
\(=\frac{6\left(8+3\sqrt6\right)}{64-54}=\frac{6\left(8+3\sqrt6\right)}{10}=\frac{3\left(8+3\sqrt6\right)}{5}\)
c: A<0
=>\(\frac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}\left(\sqrt{x}-1\right)}<0\)
=>\(\sqrt{x}-1<0\)
=>\(\sqrt{x}<1\)
=>0<x<1
Bạn nên chịu khó gõ đề ra khả năng được giúp sẽ cao hơn.
Câu h của em đây nhé
h, ( 1 + \(\dfrac{3-\sqrt{3}}{\sqrt{3}-1}\)).(1 - \(\dfrac{3+\sqrt{3}}{\sqrt{3}+1}\))
= \(\dfrac{\sqrt{3}-1+3-\sqrt{3}}{\sqrt{3}-1}\).\(\dfrac{\sqrt{3}+1-3-\sqrt{3}}{\sqrt{3}+1}\)
= \(\dfrac{2}{\sqrt{3}-1}\).\(\dfrac{-2}{\sqrt{3}+1}\)
= \(\dfrac{-4}{2}\)
= -2
\(\text{#}HaimeeOkk\)
\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{2018.2019}+\dfrac{1}{2019.2020}\)
\(A=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{2018}-\dfrac{1}{2019}+\dfrac{1}{2019}-\dfrac{1}{2020}\)
\(A=1-\left(\dfrac{1}{2}-\dfrac{1}{2}\right)-\left(\dfrac{1}{3}-\dfrac{1}{3}\right)-\left(\dfrac{1}{4}-\dfrac{1}{4}\right)-...-\left(\dfrac{1}{2019}-\dfrac{1}{2019}\right)-\dfrac{1}{2020}\)
\(A=1-0-0-0-...-0-\dfrac{1}{2020}\)
\(A=1-\dfrac{1}{2020}\)
\(A=\dfrac{2019}{2020}\)
Vậy \(A=\dfrac{2019}{2020}\)
nNa2SO4= 9,94/142=0,07(mol);
mBa(OH)2= 20,52(g) -> nBa(OH)2=0,12(mol)
PTHH: Na2SO4 + Ba(OH)2 -> BaSO4 + 2 NaOH
Ta cps: 0,07/1 < 0,12/1
=> Ba(OH)2 dư, Na2SO4 hết, tính theo nNa2SO4.
-> nBaSO4=nNa2SO4= 0,07(mol)
=> m(kết tủa)=mBaSO4=0,07.233=16,31(g)
=>m=16,31(g)
b) Dung dịch A thu được bao gồm NaOH và Ba(OH)2 dư.
nNaOH=2.0,07=0,14(mol) => mNaOH= 0,14.40=5,6(g)
nBa(OH)2 (dư)=0,12-0,07=0,05(mol)
=> mBa(OH)2 (dư)= 0,05.171=8,55(g)
=> mddA=Na2SO4 + mddBa(OH)2 - mBaSO4 = 9,94+ 100 - 16,31= 93,63(g)
=> C%ddBa(OH)2 (dư)= (8,55/93,63).100=9,132%
C%ddNaOH= (5,6/93,63).100=5,981%






