Bài 29. Làm tính trừ các phân thức sau:
a) \( \frac{4x-1}{3x^{2}y}-\frac{7x-1}{3x^{2}y}\); b) \( \frac{4x+5}{2x-1}-\frac{5-9x}{2x-1}\);
c) \( \frac{11x}{2x-3}-\frac{x-18}{3-2x}\); d) \( \frac{2x-7}{10x-4}-\frac{3x+5}{4-10x}\).
Hướng dẫn giải:
a) \( \frac{4x-1}{3x^{2}y}-\frac{7x-1}{3x^{2}y}\) \( =\frac{4x-1}{3x^{2}y}+\frac{-(7x-1)}{3x^{2}y}\)
\( =\frac{4x-1-7x+1}{3x^{2}y}\) \( =\frac{-3x}{3x^{2}y}=-\frac{1}{xy}\).
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b) \( \frac{4x+5}{2x-1}-\frac{5-9x}{2x-1}\) \( =\frac{4x+5}{2x-1}+\frac{-(5-9x)}{2x-1}\)
\( =\frac{4x+5-5+9x}{2x-1}= \frac{13x}{2x-1}\)
c) \( \frac{11x}{2x-3}-\frac{x-18}{3-2x}\) \( =\frac{11x}{2x-3}+\frac{x-18}{-(3-2x)}\)
\( =\frac{11x}{2x-3}+\frac{x-18}{2x-3}\) \( =\frac{11x+x-18}{2x-3}\) \( =\frac{12x-18}{2x-3}=6\)
d) \( \frac{2x-7}{10x-4}-\frac{3x+5}{4-10x}\) \( =\frac{2x-7}{10x-4}-\frac{3x+5}{-(4-10x)}\)
\( =\frac{2x-7}{10x-4}-\frac{3x+5}{10x-4}\) \( =\frac{2x-7+3x+5}{10x-4}\) \( =\frac{5x-2}{2(5x-2)}=\frac{1}{2}\)