Bài 21. Thực hiện các phép tính sau:
a) \( \frac{3x-5}{7}+\frac{4x+5}{7}\); b) \( \frac{5xy-4y}{2x^{2}y^{3}}+\frac{3xy+4y}{2x^{2}y^{3}}\)
c) \( \frac{x+1}{x-5}+\frac{x-18}{x-5}+\frac{x+2}{x-5}\).
Hướng dẫn giải:
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a) \( \frac{3x-5}{7}+\frac{4x+5}{7}\) = \( \frac{3x-5+4x+5}{7}=\frac{7x}{7}=x\)
b) \( \frac{5xy-4y}{2x^{2}y^{3}}+\frac{3xy+4y}{2x^{2}y^{3}}\) = \( \frac{5xy-4y+3xy+4y}{2x^{2}y^{3}}=\frac{8xy}{2x^{2}y^{3}}=\frac{4}{xy^{2}}\)
c) \( \frac{x+1}{x-5}+\frac{x-18}{x-5}+\frac{x+2}{x-5}\)= \( \frac{x+1+x-18+x+2}{x-5}=\frac{3x-15}{x-5}=\frac{3(x-5)}{x-5}=3\)