Question

\(P=\left(\dfrac{\sqrt{b}+1}{\sqrt{b}-1}-\dfrac{\sqrt{b}-1}{\sqrt{b}+1}+4\sqrt{b}\right).\dfrac{1}{2b\sqrt{b}}\)

rút gon P và tìm giá trị của b để P=b

Answer 1

\(P=\left(\dfrac{\sqrt{b}+1}{\sqrt{b}-1}-\dfrac{\sqrt{b}-1}{\sqrt{b}+1}+4\sqrt{b}\right).\dfrac{1}{2b\sqrt{b}}\);\(ĐK:b\ge0;b\ne\pm1;0\)

\(P=\left(\dfrac{\left(\sqrt{b}+1\right)^2-\left(\sqrt{b}-1\right)^2}{\left(\sqrt{b}-1\right)\left(\sqrt{b}+1\right)}+4\sqrt{b}\right).\dfrac{1}{2b\sqrt{b}}\)

\(P=\left(\dfrac{b+2\sqrt{b}+1-b+2\sqrt{b}-1}{\left(\sqrt{b}-1\right)\left(\sqrt{b}+1\right)}+4\sqrt{b}\right).\dfrac{1}{2b\sqrt{b}}\)

\(P=\dfrac{4\sqrt{b}+4\sqrt{b}\left(\sqrt{b}-1\right)\left(\sqrt{b}+1\right)}{\left(\sqrt{b}-1\right)\left(\sqrt{b}+1\right)}.\dfrac{1}{2b\sqrt{b}}\)

\(P=\dfrac{4\sqrt{b}\left(1+b-1\right)}{b-1}.\dfrac{1}{2b\sqrt{b}}\)

\(P=\dfrac{4b\sqrt{b}}{2b\sqrt{b}\left(b-1\right)}\)

\(P=\dfrac{2}{b-1}\)