Bài 29 trang 50 SGK Toán 8 tập 1

Làm tính trừ các phân thức sau:

a) \( \dfrac{4x-1}{3x^{2}y}-\dfrac{7x-1}{3x^{2}y}\);   

b) \( \dfrac{4x+5}{2x-1}-\dfrac{5-9x}{2x-1}\);

c) \( \dfrac{11x}{2x-3}-\dfrac{x-18}{3-2x}\); 

d) \( \dfrac{2x-7}{10x-4}-\dfrac{3x+5}{4-10x}\).

a) \( \dfrac{4x-1}{3x^{2}y}-\dfrac{7x-1}{3x^{2}y}\) \( =\dfrac{4x-1}{3x^{2}y}+\dfrac{-(7x-1)}{3x^{2}y}\)

\( =\dfrac{4x-1-7x+1}{3x^{2}y}\) \( =\dfrac{-3x}{3x^{2}y}=-\dfrac{1}{xy}\).

b) \( \dfrac{4x+5}{2x-1}-\dfrac{5-9x}{2x-1}\) \( =\dfrac{4x+5}{2x-1}+\dfrac{-(5-9x)}{2x-1}\)

\( =\dfrac{4x+5-5+9x}{2x-1}= \dfrac{13x}{2x-1}\)

c) \( \dfrac{11x}{2x-3}-\dfrac{x-18}{3-2x}\) \( =\dfrac{11x}{2x-3}+\dfrac{x-18}{-(3-2x)}\)

\( =\dfrac{11x}{2x-3}+\dfrac{x-18}{2x-3}\) \( =\dfrac{11x+x-18}{2x-3}\)

\( =\dfrac{12x-18}{2x-3}=\dfrac{{6\left( {2x - 3} \right)}}{{2x - 3}}=6\)

d) \( \dfrac{2x-7}{10x-4}-\dfrac{3x+5}{4-10x}\) \( =\dfrac{2x-7}{10x-4}+\dfrac{3x+5}{-(4-10x)}\)

\( =\dfrac{2x-7}{10x-4}+\dfrac{3x+5}{10x-4}\)\( =\dfrac{2x-7+3x+5}{10x-4}\)\( =\dfrac{5x-2}{2(5x-2)}=\dfrac{1}{2}\)