Question

rút gọn Q = \(\frac{\sqrt{a}+3}{\sqrt{a}-2}\)- \(\frac{\sqrt{a}-1}{\sqrt{a}+2}\)+ \(\frac{4\sqrt{a}-4}{4-a}\)

Answer 1

Q = \(\frac{\sqrt{a}+3}{\sqrt{a}-2}\)- \(\frac{\sqrt{a}-1}{\sqrt{a}+2}\)+ \(\frac{4-4\sqrt{a}}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\)

  = \(\frac{\left(\sqrt{a}+3\right)\left(\sqrt{a}+2\right)-\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)+4-4\sqrt{a}}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\)

   =\(\frac{a+5\sqrt{a}+6-a+3\sqrt{a}-2+4-4\sqrt{a}}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\)

  = \(\frac{8+4\sqrt{a}}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\)

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

  = \(\frac{4}{\sqrt{a}-2}\)

Answer 2

\(Q=\frac{\sqrt{a+3}}{\sqrt{a-2}}-\frac{\sqrt{a-1}}{\sqrt{a+2}}+\frac{4-4\sqrt{a}}{\left(\sqrt{a-2}\right)\left(\sqrt{a+2}\right)}\)

\(Q=\frac{\left(\sqrt{a+3}\right)\left(\sqrt{a+2}\right)-\left(\sqrt{a-1}\right)\left(\sqrt{a-2}\right)+4-4\sqrt{a}}{\left(\sqrt{a-2}\right)\left(\sqrt{a+2}\right)}\)

\(Q=\frac{a+5\sqrt{a}+6-a+3\sqrt{a-2}+4-4\sqrt{a}}{\left(\sqrt{a-2}\right)\left(\sqrt{a+2}\right)}\)

\(Q=\frac{8+4\sqrt{a}}{\left(\sqrt{a-2}\right)\left(\sqrt{a+2}\right)}\)

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

\(Q=\frac{4}{\sqrt{a-2}}\)