Giải bài 29 trang 50 – SGK Toán lớp 8 tập 1
Làm tính trừ các phân thức sau:
a) \(\dfrac{4x - 1}{3x^2y} - \dfrac{7x - 1}{3x^2 y}\)
b) \(\dfrac{4x + 5}{2x - 1} - \dfrac{5 - 9x}{2x - 1}\)
c) \(\dfrac{11x}{2x - 3} - \dfrac{x - 18}{3 - 2x}\)
d) \(\dfrac{2x - 7}{10x - 4} - \dfrac{3x + 5}{4 - 10x}\)
Hướng dẫn:
Muốn trừ phân thức \(\dfrac{A}{B}\) cho phân thức \(\dfrac{C}{D},\) ta cộng \(\dfrac{A}{B}\) với phân thức đối của \(\dfrac{C}{D}:\)
\(\dfrac{A}{B} - \dfrac{C}{D} = \dfrac{A}{B} + \left(-\dfrac{C}{D}\right)\)
Bài giải
a) \(\dfrac{4x - 1}{3x^2y} - \dfrac{7x - 1}{3x^2y}\)
\(= \dfrac{4x - 1}{3x^2y} + \dfrac{-(7x - 1)}{3x^2 - 1}\)
\(= \dfrac{4x - 1}{3x^2y} + \dfrac{-7x + 1}{3x^2 - 1}\)
\(= \dfrac{(4x - 1) + (-7x + 1)}{3x^2y}\)
\(= \dfrac{4x - 1 - 7x + 1}{3x^2y}\)
\(= \dfrac{-3x}{3x^2y}\)
\(= \dfrac{-1}{xy}\)
b) \(\dfrac{4x + 5}{2x - 1} - \dfrac{5 - 9x}{2x - 1}\)
\(= \dfrac{4x + 5}{2x - 1} + \dfrac{-(5 - 9x)}{2x - 1}\)
\(= \dfrac{4x + 5}{2x - 1} + \dfrac{-5 + 9x}{2x - 1}\)
\(= \dfrac{(4x + 5) + (-5 + 9x)}{2x - 1}\)
\(= \dfrac{4x + 5 - 5 + 9x}{2x - 1}\)
\(= \dfrac{13x}{2x - 1}\)
c) \(\dfrac{11x}{2x - 3} - \dfrac{x - 18}{3 - 2x}\)
\(= \dfrac{11x}{2x - 3} + \dfrac{x - 18}{-(3 - 2x)}\)
\(= \dfrac{11x}{2x - 3} + \dfrac{x - 18}{2x - 3}\)
\(= \dfrac{11x + x - 18}{2x - 3}\)
\(= \dfrac{12x - 18}{2x - 3} \)
\(= \dfrac{6(2x - 3)}{2x - 3} \)
\(= 6\)
d) \(\dfrac{2x - 7}{10x - 4} - \dfrac{3x + 5}{4 - 10x}\)
\(= \dfrac{2x - 7}{10x - 4} + \dfrac{3x + 5}{-(4 - 10x)}\)
\(= \dfrac{2x - 7}{10x - 4} + \dfrac{3x + 5}{10x - 4}\)
\(= \dfrac{2x - 7 + 3x + 5}{10x - 4}\)
\(= \dfrac{5x - 2}{2(5x - 2)}\)
\(= \dfrac{1}{2}\)