Tìm tập nghiệm của bất phương trình  \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaGaaGOnaiGacYgacaGGVbGaai4zamaaBaaaleaacaaIYaaabeaa % kiaadIhaaeaaciGGSbGaai4BaiaacEgadaWgaaWcbaGaaGOmaaqaba % GccaWG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaG4maaaacqGH % sisldaWcaaqaaiaaiodaciGGSbGaai4BaiaacEgadaWgaaWcbaGaaG % OmaaqabaGccaWG4bWaaWbaaSqabeaacaaIYaaaaaGcbaGaciiBaiaa % c+gacaGGNbWaaSbaaSqaaiaaikdaaeqaaOGaamiEaiabgUcaRiaaig % daaaGaeyipaWJaaGimaiaac6caaaa!53C7! \frac{{16{{\log }_2}x}}{{{{\log }_2}{x^2} + 3}} - \frac{{3{{\log }_2}{x^2}}}{{{{\log }_2}x + 1}} < 0.\)

Đặt \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiabg2 % da9iGacYgacaGGVbGaai4zamaaBaaaleaacaaIYaaabeaakiaadIha % aaa!3CB2! t = {\log _2}x\). bất phương trình trở thành

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca % aIXaGaaGOnaiaadshaaeaacaaIYaGaamiDaiabgUcaRiaaiodaaaGa % eyOeI0YaaSaaaeaacaaI2aGaamiDaaqaaiaadshacqGHRaWkcaaIXa % aaaiabgYda8iaaicdacqGHuhY2daWcaaqaaiaaikdacaWG0bWaaeWa % aeaacaaIYaGaamiDaiabgkHiTiaaigdaaiaawIcacaGLPaaaaeaada % qadaqaaiaaikdacaWG0bGaey4kaSIaaG4maaGaayjkaiaawMcaamaa % bmaabaGaamiDaiabgUcaRiaaigdaaiaawIcacaGLPaaaaaGaeyipaW % JaaGimaiabgsDiBpaadeaaeaqabeaadaWcaaqaaiabgkHiTiaaioda % aeaacaaIYaaaaiabgYda8iaadshacqGH8aapcqGHsislcaaIXaaaba % GaaGimaiabgYda8iaadshacqGH8aapdaWcaaqaaiaaigdaaeaacaaI % YaaaaaaacaGLBbaaaaa!6656! \frac{{16t}}{{2t + 3}} - \frac{{6t}}{{t + 1}} < 0 \Leftrightarrow \frac{{2t\left( {2t - 1} \right)}}{{\left( {2t + 3} \right)\left( {t + 1} \right)}} < 0 \Leftrightarrow \left[ \begin{array}{l} \frac{{ - 3}}{2} < t < - 1\\ 0 < t < \frac{1}{2} \end{array} \right.\)

Khi đó \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamqaaqaabe % qaamaalaaabaGaeyOeI0IaaG4maaqaaiaaikdaaaGaeyipaWJaciiB % aiaac+gacaGGNbWaaSbaaSqaaiaaikdaaeqaaOGaamiEaiabgYda8i % abgkHiTiaaigdaaeaacaaIWaGaeyipaWJaciiBaiaac+gacaGGNbWa % aSbaaSqaaiaaikdaaeqaaOGaamiEaiabgYda8maalaaabaGaaGymaa % qaaiaaikdaaaaaaiaawUfaaiabgsDiBpaadeaaeaqabeaadaWcaaqa % aiaaigdaaeaacaaIYaWaaOaaaeaacaaIYaaaleqaaaaakiabgYda8i % aadIhacqGH8aapdaWcaaqaaiaaigdaaeaacaaIYaaaaaqaaiaaigda % cqGH8aapcaWG4bGaeyipaWZaaOaaaeaacaaIYaaaleqaaaaakiaawU % faaaaa!59D6! \left[ \begin{array}{l} \frac{{ - 3}}{2} < {\log _2}x < - 1\\ 0 < {\log _2}x < \frac{1}{2} \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} \frac{1}{{2\sqrt 2 }} < x < \frac{1}{2}\\ 1 < x < \sqrt 2 \end{array} \right.\)