Chọn câu đúng? A. 1/(x-2)-1/((x+2)(4x+7))=4x/(x+2)(4x+7)

* Hướng dẫn giải

* $\begin{array}{l}\frac{1}{\mathrm{x}+2}-\frac{1}{(\mathrm{x}+2\left)\right(4\mathrm{x}+7)}=\frac{1.(4\mathrm{x}+7)}{(\mathrm{x}+2\left)\right(4\mathrm{x}+7)}-\frac{1}{(\mathrm{x}+2\left)\right(4\mathrm{x}+7)}\\ =\frac{4\mathrm{x}+7-1}{(\mathrm{x}+2\left)\right(4\mathrm{x}+7)}=\frac{4\mathrm{x}+6}{(\mathrm{x}+2\left)\right(4\mathrm{x}+7)}\end{array}$

nên A sai.

* $\begin{array}{l}\frac{2-21\mathrm{x}}{18}-\frac{4+\mathrm{x}}{12}=\frac{2(2-21\mathrm{x})}{18.2}-\frac{3(4+\mathrm{x})}{12.3}\\ =\frac{4-42\mathrm{x}-12-3\mathrm{x}}{36}=\frac{-45\mathrm{x}-8}{36}\end{array}$

nên B sai

* $\begin{array}{l}\frac{1}{\mathrm{x}+4}-\frac{1}{\mathrm{x}+5}=\frac{\mathrm{x}+5}{(\mathrm{x}+4\left)\right(\mathrm{x}+5)}-\frac{\mathrm{x}+4}{(\mathrm{x}+4\left)\right(\mathrm{x}+5)}\\ =\frac{\mathrm{x}+5-\mathrm{x}-4}{(\mathrm{x}+4\left)\right(\mathrm{x}+5)}=\frac{1}{(\mathrm{x}+4\left)\right(\mathrm{x}+5)}\end{array}$

nên C đúng

* $\begin{array}{l}\frac{2}{\mathrm{x}-5}+\frac{3\mathrm{x}}{{\mathrm{x}}^2-25}=\frac{2(\mathrm{x}+5)}{(\mathrm{x}-5)(\mathrm{x}+5)}+\frac{3\mathrm{x}}{(\mathrm{x}-5\left)\right(\mathrm{x}+5)}\\ =\frac{2\mathrm{x}+10+3\mathrm{x}}{(\mathrm{x}-5\left)\right(\mathrm{x}+5)}=\frac{5\mathrm{x}+10}{(\mathrm{x}-5\left)\right(\mathrm{x}+5)}\end{array}$

nên D sai.

Đáp án cần chọn là: C