(2đ) Quy đồng mẫu thức các

- Hướng dẫn giải

Phương pháp giải:

Giải chi tiết:

\(\begin{array}{l}
a)A = \frac{5}{{2x - 4}};B = \frac{4}{{3x - 9}};C = \frac{7}{{10 - 5x}}\\
2x - 4 = 2(x - 2)\\
3x - 9 = 3(x - 3)\\
10 - 5x = 5(2 - x)\\
MTC:2.3.5(x - 2)(x - 3) = 30(x - 2)(x - 3)\\
A = \frac{5}{{2x - 4}} = \frac{{5.3.5(x - 3)}}{{30(x - 2)(x - 3)}} = \frac{{75(x - 3)}}{{30(x - 2)(x - 3)}} = \frac{{75x - 225}}{{30(x - 2)(x - 3)}}\\
B = \frac{4}{{3x - 9}} = \frac{{4.2.5(x - 2)}}{{30(x - 2)(x - 3)}} = \frac{{40(x - 2)}}{{30(x - 2)(x - 3)}} = \frac{{40x - 80}}{{30(x - 2)(x - 3)}}\\
C = \frac{7}{{10 - 5x}} = \frac{{ - 7}}{{5(x - 2)}} = \frac{{ - 7.2.3(x - 3)}}{{30(x - 2)(x - 3)}} = \frac{{ - 42(x - 3)}}{{30(x - 2)(x - 3)}} = \frac{{ - 42x + 126}}{{30(x - 2)(x - 3)}}\\
b)D = \frac{{{x^2}}}{{{x^2} - 1}};E = \frac{{3x - 1}}{{{x^3} + 2{x^2} + x}};F = \frac{{2x + 1}}{{{x^3}}}\\
{x^2} - 1 = (x - 1)(x + 1)\\
{x^3} + 2{x^2} + x = x({x^2} + 2x + 1) = x{(x + 1)^2}\\
MTC:{x^3}{(x + 1)^2}(x - 1)\\
D = \frac{{{x^2}}}{{{x^2} - 1}} = \frac{{{x^2}}}{{(x - 1)(x + 1)}} = \frac{{{x^2}.{x^3}\left( {x + 1} \right)}}{{{x^3}{{(x + 1)}^2}(x - 1)}} = \frac{{{x^5}(x + 1)}}{{{x^3}{{(x + 1)}^2}(x - 1)}}\\
E = \frac{{3x - 1}}{{{x^3} + 2{x^2} + x}} = \frac{{3x - 1}}{{x{{(x + 1)}^2}}} = \frac{{(3x - 1){x^2}(x - 1)}}{{{x^3}{{(x + 1)}^2}(x - 1)}}\\
F = \frac{{2x + 1}}{{{x^3}}} = \frac{{(2x + 1)(x - 1){{(x + 1)}^2}}}{{{x^3}{{(x + 1)}^2}(x - 1)}}
\end{array}\)