Question

Rút gọn các biểu thức sau:

a,\(\frac{b-16}{4-\sqrt{b}}\)    \(\left(b\ge0;b\ne16\right)\)

b,\(\frac{a-4\sqrt{a}+4}{a-4}\)  \(\left(a\ge0;a\ne4\right)\)

c,\(2x+\sqrt{1+4x^2-4x}\)  \(\left(x\le\frac{1}{2}\right)\)

d,\(\frac{4a-4b}{\sqrt{a}-\sqrt{b}}\)  \(\left(a,b\ge0;a\ne b\right)\)

Giúp mình với nha!

Answer 1

làm sao viết đc căn vs phân số v mấy bn

Answer 2

a) \(\frac{b-16}{4-\sqrt{b}}\left(b\ge0,b\ne16\right)\)

\(=\frac{\left(\sqrt{b}-4\right)\left(\sqrt{b}+4\right)}{4-\sqrt{b}}\)

\(=-\sqrt{b}-4\)

b) \(\frac{a-4\sqrt{a}+4}{a-4}\left(a\ge0;a\ne4\right)\)

\(=\frac{a-2.\sqrt{a}.2+4}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\)

\(=\frac{\left(\sqrt{a}-2\right)^2}{\left(\sqrt{a}+2\right)\left(\sqrt{a}-2\right)}=\frac{\sqrt{a}-2}{\sqrt{a}+2}\)

c) \(2x+\sqrt{1+4x^2-4x}\) với \(x\le\frac{1}{2}\)

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

\(=2x+\left|1-2x\right|=2x+1-2x=1\)

d) \(\frac{4a-4b}{\sqrt{a}-\sqrt{b}}\left(a,b\ge0;a\ne b\right)\)

\(=\frac{4\left(a-b\right)}{\sqrt{a}-\sqrt{b}}=\frac{4\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{a}-\sqrt{b}}\)

\(=4\left(\sqrt{a}+\sqrt{b}\right)\)