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23 tháng 4 2021

\(\frac{1}{3-\sqrt{7}}-\frac{1}{3+\sqrt{7}}=\frac{3+\sqrt{7}}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}-\frac{3-\sqrt{7}}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}\)

\(=\frac{3+\sqrt{7}-3+\sqrt{7}}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}=\frac{2\sqrt{7}}{9-7}=\sqrt{7}\)

23 tháng 4 2021

a, \(\frac{1}{3-\sqrt{7}}-\frac{1}{3+\sqrt{7}}=\frac{3+\sqrt[]{7}-3+\sqrt{7}}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}\)

\(=\frac{2\sqrt{7}}{9-7}=\sqrt{7}\)

19 tháng 7 2019

\(A=\frac{7}{3+\sqrt{2}}+\frac{2}{1-\sqrt{3}}\)

\(=\frac{7\left(3-\sqrt{2}\right)}{3^2-\sqrt{2}^2}+\frac{2\left(1+\sqrt{3}\right)}{1^2-\sqrt{3}^2}\)

\(=\frac{7\left(3-\sqrt{2}\right)}{7}+\frac{2\left(1+\sqrt{3}\right)}{-2}\)

\(=3-\sqrt{2}-1-\sqrt{3}\)

\(=2-\sqrt{2}-\sqrt{3}\)

18 tháng 10 2020

\(A=\frac{7}{3+\sqrt{2}}+\frac{2}{1-\sqrt{3}}=\frac{7\left(3-\sqrt{2}\right)}{3^2-\left(\sqrt{2}\right)^2}+\frac{2\left(1+\sqrt{3}\right)}{1^2-\left(\sqrt{3}\right)^2}\)

\(=\frac{7\left(3-\sqrt{2}\right)}{9-2}+\frac{2\left(1+\sqrt{3}\right)}{1-3}=\frac{7\left(3-\sqrt{2}\right)}{7}+\frac{2\left(1+\sqrt{3}\right)}{-2}\)

\(=\left(3-\sqrt{2}\right)-\left(1+\sqrt{3}\right)=3-\sqrt{2}-1-\sqrt{3}=2-\sqrt{2}-\sqrt{3}\)

5 tháng 7 2019

Mọi người giải chi tiết giúp mình

5 tháng 7 2019

\(\frac{1}{3-\sqrt{7}}-\frac{1}{3+\sqrt{7}}\)

\(=\frac{3+\sqrt{7}}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}-\frac{3-\sqrt{7}}{\left(3+\sqrt{7}\right)\left(3-\sqrt{7}\right)}\)

\(=\frac{3+\sqrt{7}-3+\sqrt{7}}{9-7}\)

\(=\frac{2\sqrt{7}}{2}\)

\(=\sqrt{7}\)

phần B là gì cơ?

28 tháng 7 2017

\(P=\frac{x+2}{\sqrt{x}^3-1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(P=\frac{x+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{1}{\sqrt{x}-1}\)

\(P=\frac{x+2+x-1-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)

2,

\(A=\frac{5\left(\sqrt{7}-\sqrt{2}\right)}{\left(\sqrt{7}-\sqrt{2}\right)\left(\sqrt{7}+\sqrt{2}\right)}+\frac{\sqrt{2}+1}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}-\frac{7\sqrt{7}}{7}\)

\(A=\frac{5\left(\sqrt{7}-\sqrt{2}\right)}{7-2}+\frac{\left(\sqrt{2}+1\right)}{2-1}-\sqrt{7}\)

\(A=\sqrt{7}-\sqrt{2}+\sqrt{2}+1-\sqrt{7}=1\)

\(P=\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\frac{\sqrt{x}}{x+\sqrt{x}+1}\)

NM
9 tháng 9 2021

\(\frac{3}{\sqrt{7}-1}+\frac{3}{\sqrt{7}+1}=\frac{3\left[\sqrt{7}+1+\sqrt{7}-1\right]}{\left(\sqrt{7}+1\right)\left(\sqrt{7}-1\right)}=\frac{6\sqrt{7}}{6}=\sqrt{7}\)

\(\frac{3}{\sqrt{X}-1}-\frac{2}{\sqrt{X}+1}+\frac{X-7}{X-1}=\frac{3\left(\sqrt{X}+1\right)-2\left(\sqrt{X}-1\right)+X-7}{\left(\sqrt{X}+1\right)\left(\sqrt{X}-1\right)}=\frac{X+\sqrt{X}-2}{\left(\sqrt{X}+1\right)\left(\sqrt{X}-1\right)}=\frac{\sqrt{X}+2}{\sqrt{X}+1}\)

9 tháng 9 2021

TÍNH GIÁ TRỊ BIỂU THỨC:

\(\frac{3}{\sqrt{7}-1}\) + \(\frac{3}{\sqrt{7}+1}\)\(\frac{3\left(\sqrt{7}+1\right)+3\left(\sqrt{7}-1\right)}{\left(\sqrt{7}-1\right)\left(\sqrt{7}+1\right)}\)\(\frac{3\sqrt{7}+3+3\sqrt{7}-3}{6}\)=\(\frac{6\sqrt{7}}{6}\)=\(\sqrt{7}\)

RÚT GỌN BIỂU THỨC:

\(\frac{3}{\sqrt{X}-1}\)-\(\frac{2}{\sqrt{X}+1}\)+\(\frac{X-7}{X-1}\)

\(\frac{3\left(\sqrt{X}+1\right)}{\left(\sqrt{X}-1\right)\left(\sqrt{X}+1\right)}\)-\(\frac{2\left(\sqrt{X}-1\right)}{\left(\sqrt{X}-1\right)\left(\sqrt{X}+1\right)}\)+\(\frac{X-7}{\left(\sqrt{X}-1\right)\left(\sqrt{X}+1\right)}\)

\(\frac{3\sqrt{X}+3-2\sqrt{X}+2+X-7}{\left(\sqrt{X}-1\right)\left(\sqrt{X}+1\right)}\)

\(\frac{X+\sqrt{X}-2}{\left(\sqrt{X}-1\right)\left(\sqrt{X}+1\right)}\)

\(\frac{\left(\sqrt{X}+1\right)\left(\sqrt{X}-2\right)}{\left(\sqrt{X}-1\right)\left(\sqrt{X}+1\right)}\)

\(\frac{\sqrt{X}-2}{\sqrt{X}-1}\)

CHÚC EM HỌC TỐT!

31 tháng 5 2018

Tu bieu thuc \(\Leftrightarrow\frac{3.\left(\sqrt{7}+2\right)}{\left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right)}-\frac{14\sqrt{7}}{7}+|\sqrt{7}-2|\)

                    \(\Leftrightarrow3\sqrt{7}+6-2\sqrt{7}+\sqrt{7}-2=2\sqrt{7}+4\)

3 tháng 9 2020

Ta đặt: \(A=\sqrt{\sqrt{7}-\sqrt{3}}-\sqrt{\sqrt{7}+\sqrt{3}}\)

=> \(A^2=\left(\sqrt{\sqrt{7}-\sqrt{3}}-\sqrt{\sqrt{7}+\sqrt{3}}\right)^2\)

<=> \(A^2=\sqrt{7}-\sqrt{3}-2\sqrt{\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)}+\sqrt{7}+\sqrt{3}\)

<=> \(A^2=2\sqrt{7}-2\sqrt{7-3}\)

<=> \(A^2=2\sqrt{7}-2\sqrt{4}=2\left(\sqrt{7}-2\right)\)

=> \(A=\sqrt{2\left(\sqrt{7}-2\right)}\)

Thay vào ta được:

\(\frac{\sqrt{2\left(\sqrt{7}-2\right)}}{\sqrt{\sqrt{7}-2}}=\sqrt{2}\)