Bài 21 trang 46 sách giáo khoa toán 7 tập 1
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:
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]\[ \frac{x+1}{x-5}+\frac{x-18}{x-5}+\frac{x+2}{x-5}\]=\[ \frac{x+1+x-18+x+2}{x-5}=\frac{3x-15}{x-5}=\frac{3[x-5]}{x-5}=3\]
Bài 22 trang 46 sách giáo khoa toán 8 tập 1
Áp dụng quy tắc đổi dấu để các phân thức có cùng mẫu thức rồi làm tính cộng phân thức.
a]\[ \frac{2x^{2}-x}{x-1}+\frac{x+1}{1-x}+\frac{2-x^{2}}{x-1}\];
b]\[ \frac{4-x^{2}}{x-3}+\frac{2x-2x^{2}}{3-x}+\frac{5-4x}{x-3}\].
Hướng dẫn giải:
a]\[ \frac{2x^{2}-x}{x-1}+\frac{x+1}{1-x}+\frac{2-x^{2}}{x-1}\]=\[ \frac{2x^{2}-x}{x-1}+\frac{-[x+1]}{[x-1]}+\frac{2-x^{2}}{x-1}\]
\[=\frac{2x^{2}-x}{x-1}+\frac{-x-1}{x-1}+\frac{2-x^{2}}{x-1}\]
\[=\frac{2x^{2}-x-x-1+2-x^{2}}{x-1}=\frac{x^{2}-2x+1}{x-1}=x-1\]
b]\[ \frac{4-x^{2}}{x-3}+\frac{2x-2x^{2}}{3-x}+\frac{5-4x}{x-3}\]
\[ =\frac{4-x^{2}}{x-3}+\frac{-[2x-2x^{2}]}{x-3}+\frac{5-4x}{x-3}\]
\[ =\frac{4-x^{2}}{x-3}+\frac{2x^{2}-2x}{x-3}+\frac{5-4x}{x-3}\]
\[ =\frac{4-x^{2}+2x^{2}-2x+5-4x}{x-3}=\frac{x^{2}-6x+9}{x-3}\]
\[ =\frac{[x-3]^{2}}{x-3}= x-3\]
Bài 23 trang 46 sách giáo khoa toán 8 tập 1
Làm các phép tính sau.
a]\[ \frac{y}{2x^{2}-xy}+\frac{4x}{y^{2}-2xy}\];
b]\[ \frac{1}{x+2}+\frac{3}{x^{2}-4}+\frac{x-14}{[x^{2}+4x+4][x-2]}\];
c]\[ \frac{1}{x+2}+\frac{1}{[x+2][4x+7]}\];
d]\[ \frac{1}{x+3}+\frac{1}{[x+3][x+2]}+\frac{1}{[x+2][4x+7]}\]
Giải
a]\[ \frac{y}{2x^{2}-xy}+\frac{4x}{y^{2}-2xy}\]\[ =\frac{y}{x[2x-y]}+\frac{4x}{y[y-2x]}\]
\[ =\frac{y}{x[2x-y]}+\frac{-4x}{y[2x-y]}=\frac{y^{2}}{xy[2x-y]}+\frac{-4x^{2}}{xy[2x-y]}\]
=\[ \frac{y^{2}-4x^{2}}{xy[2x-y]}=\frac{[y-2x][y+2x]}{xy[2x-y]}=\frac{-[2x-y][y+2x]}{xy[2x-y]}\]
\[ =\frac{-[2x+y]}{xy}\]
b]\[ \frac{1}{x+2}+\frac{3}{x^{2}-4}+\frac{x-14}{[x^{2}+4x+4][x-2]}\]
\[ =\frac{1}{x+2}+\frac{3}{[x-2][x+2]}+\frac{x-14}{[x+2]^{2}[x-2]}\]
\[ =\frac{[x+2][x-2]}{[x+2]^{2}[x-2]}+\frac{3[x+2]}{[x-2][x+2]^{2}}+\frac{x-14}{[x+2]^{2}[x-2]}\]
\[ =\frac{x^{2}-4+3x+6+x-14}{[x+2]^{2}[x-2]}= \frac{x^{2}+4x-12}{[x+2]^{2}[x-2]}\]
\[ =\frac{x^{2}-2x+6x-12}{[x+2]^{2}[x-2]}= \frac{x[x-2]+6[x-2]}{[x+2]^{2}[x-2]}\]
\[ = \frac{[x-2][x+6]}{[x+2]^{2}[x-2]}=\frac{x+6}{[x+2]^{2}}\]
c]\[ \frac{1}{x+2}+\frac{1}{[x+2][4x+7]}\]
\[ =\frac{4x+7}{[x+2][4x+7]}+\frac{1}{[x+2][4x+7]}\]
\[ =\frac{4x+8}{[x+2][4x+7]}=\frac{4[x+2]}{[x+2][4x+7]}=\frac{4}{4x+7}\]
d]\[ \frac{1}{x+3}+\frac{1}{[x+3][x+2]}+\frac{1}{[x+2][4x+7]}\]
\[ =\frac{x+2}{[x+3][x+2]}+\frac{1}{[x+3][x+2]}+\frac{1}{[x+2][4x+7]}\]
\[ =\frac{x+3}{[x+3][x+2]}+\frac{1}{[x+2][4x+7]}\]\[ =\frac{1}{x+2}+\frac{1}{[x+2][4x+7]}\]
\[ =\frac{4x+7}{[x+2][4x+7]}+\frac{1}{[x+2][4x+7]}=\frac{4x+8}{[x+2][4x+7]}\]
\[ =\frac{4[x+2]}{[x+2][4x+7]}=\frac{4}{4x+7}\]