Question

[~ ~ ~Bim~ ~ ~♌ Leo ♌~ ~ ~Bim~ ~ ~]

Cho biểu thức:

    \(A=\frac{\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}+1\right)}-\frac{\sqrt{x}-3}{\sqrt{x}\left(\sqrt{x}-1\right)}\)    với \(x>0\)và \(x\ne1\)

a) Rút gọn A

b) Tìm x để A = 7

Mọi người giúp mình với

Ai làm đúng thì mình kick cho 3 kick

Cảm ơn mọi người!!!!!

Answer 1

[KAl(SO4)2·12H2O]

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

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

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

\(A=\frac{4\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)

\(A=\frac{4\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)

\(A=\frac{4}{x-1}\)

b) \(\frac{4}{x-1}=7\)

\(\Leftrightarrow4=7.\left(x-1\right)\)

\(\Leftrightarrow\frac{4}{7}=x-1\)

\(\Leftrightarrow\frac{4}{7}+1=x\)

\(\Leftrightarrow\frac{11}{7}=x\)

\(\Rightarrow x=\frac{11}{7}\)