Question

Bài 4: Cho 2 phân thức A = \(\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\) và B = \(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\). Tìm x để \(\dfrac{A}{B}\)=\(\dfrac{4}{3}\)

Answer 1

\(\dfrac{A}{B}=\dfrac{4}{3}\\ =>\left(\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\right):\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\right)=\dfrac{4}{3}\left(x\ge0;x\ne1\right)\\ < =>\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\cdot\dfrac{\sqrt{x}+1}{\sqrt{x}-1}=\dfrac{4}{3}\\ < =>\dfrac{\sqrt{x}+2}{\sqrt{x}-1}=\dfrac{4}{3}\\ < =>3\left(\sqrt{x}+2\right)=4\left(\sqrt{x}-1\right)\\ < =>3\sqrt{x}+6=4\sqrt{x}-4\\ < =>4\sqrt{x}-3\sqrt{x}=6+4\\ < =>\sqrt{x}=10\\ < =>x=10^2=100\left(tm\right)\)