Question

RÚT GỌN CÁC BIỂU THỨC SAU
M = \(\dfrac{a-1}{\sqrt{a}-1}\)
N =\(\dfrac{a-1}{\sqrt{a}+1}\)
P=\(\dfrac{a\sqrt{a}-1}{\sqrt{a}-1}\)
Q=\(\dfrac{a\sqrt{a}+1}{\sqrt{a}+1}\)

Answer 1

ĐK: a > 0, a khác 1

\(M=\dfrac{a-1}{\sqrt{a}-1}=\dfrac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\sqrt{a}-1}=\sqrt{a}+1\)

\(N=\dfrac{a-1}{\sqrt{a}+1}=\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}{\sqrt{a}+1}=\sqrt{a}-1\)

\(P=\dfrac{a\sqrt{a}-1}{\sqrt{a}-1}=\dfrac{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}{\sqrt{a}-1}=a+\sqrt{a}+1\)

\(Q=\dfrac{a\sqrt{a}+1}{\sqrt{a}+1}=\dfrac{\left(\sqrt{a}+1\right)\left(a-\sqrt{a}+1\right)}{\sqrt{a}+1}=a-\sqrt{a}+1\)