So sánh $A = \dfrac{{{2^5}.7 + {2^5}}}{{{2^5}{{.5}^2} - {2^5}.3}}$ và $B = \dfrac{{{3^4}.5 - {3^6}}}{{{3^4}.13 +…

Phương pháp giải:

Rút gọn phân số

Quy đồng rồi so sánh hai phân số.

Lời giải chi tiết:

$\dfrac{{{2^5}.7 + {2^5}}}{{{2^5}{{.5}^2} - {2^5}.3}} = \dfrac{{{2^5}.(7 + 1)}}{{{2^5}.({5^2} - 3)}}$$= \dfrac{{{2^5}.(7 + 1)}}{{{2^5}.(25 - 3)}} = \dfrac{{{2^5}.8}}{{{2^5}.22}} = \dfrac{8}{{22}} = \dfrac{4}{{11}}$

$\dfrac{{{3^4}.5 - {3^6}}}{{{3^4}.13 + {3^4}}} = \dfrac{{{3^4}.(5 - {3^2})}}{{{3^4}.(13 + 1)}}$ $= \dfrac{{{3^4}.(5 - 9)}}{{{3^4}.14}} = \dfrac{{{3^4}.( - 4)}}{{{3^4}.14}} = \dfrac{{ - 4}}{{14}} = \dfrac{{ - 2}}{7}$

$MSC = 77$

$\dfrac{4}{{11}} = \dfrac{{4.7}}{{11.7}} = \dfrac{{28}}{{77}};$ $\dfrac{{ - 2}}{7} = \dfrac{{ - 2.11}}{{7.11}} = \dfrac{{ - 22}}{{77}}$

Do đó $\dfrac{{ - 22}}{{77}} \lt \dfrac{{28}}{{77}} \lt 1$ hay $B \lt A \lt 1$.