Đề thi online - Cộng, trừ các phân thức đại số - Có lời giải chi tiết

Câu 1 : Kết quả của phép tính \(\frac{3x-1}{2xy}-\frac{5x+2}{2xy}\) là:

A \(\frac{-2x-1}{2xy}\)

B \(\frac{-2x+1}{xy}\)

C \(\frac{-2x-3}{2xy}\)

D \(\frac{-2x-1}{xy}\)

Câu 2 : Điền vào chỗ trống: \(\frac{2x-6}{x+3}-.....=\frac{x+1}{2}\).

A \(\frac{-{{x}^{2}}+15}{2(x+3)}\)

B \(\frac{{{x}^{2}}-15}{2(x+3)}\)

C \(\frac{-{{x}^{2}}-15}{2(x+3)}\)

D

Cả A, B, C đều sai

Câu 3 : Thực hiện phép tính :\(\begin{align} & a)\frac{3x-4}{4{{x}^{2}}{{y}^{5}}}+\frac{9x+4}{4{{x}^{2}}{{y}^{5}}} \\& b)\frac{x+8}{x-1}-\frac{2x-1}{x-1}-\frac{6x+2}{x-1} \\ & c)\frac{5{{x}^{2}}}{5x-6}+\frac{{{x}^{2}}-1}{6-5x}-\frac{7+x-{{x}^{2}}}{5x-6} \\\end{align}\)

A \(\begin{array}{l}
a)\,\,\frac{3}{{x{y^5}}}\\
b)\,\, 7\\
c)\,\,x + 1
\end{array}\)

B \(\begin{array}{l}
a)\,\,\frac{3}{{x{y^5}}}\\
b)\,\, - 7\\
c)\,\,x + 1
\end{array}\)

C \(\begin{array}{l}
a)\,\,\frac{3}{{x{y^4}}}\\
b)\,\, - 7\\
c)\,\,x + 1
\end{array}\)

D \(\begin{array}{l}
a)\,\,\frac{3}{{x{y^5}}}\\
b)\,\, 7\\
c)\,\,x - 1
\end{array}\)

Câu 4 : Rút gọn biểu thức:\(\begin{align} & a)\frac{1}{x+2}+\frac{1}{(x+1)(x+2)}+\frac{1}{(x+1)(2x+1)} \\& b)\frac{4{{x}^{2}}-3x+5}{{{x}^{3}}-1}-\frac{1-2x}{{{x}^{2}}+x+1}-\frac{6}{x-1} \\ \end{align}\)

A \(\begin{array}{l}
a)\,\,\,-\frac{2}{{2x + 1}}\\
b)\,\,\frac{{ 12x}}{{{x^3} - 1}}
\end{array}\)

B \(\begin{array}{l}
a)\,\,\,-\frac{2}{{2x + 1}}\\
b)\,\,\frac{{ - 12x}}{{{x^3} - 1}}
\end{array}\)

C \(\begin{array}{l}
a)\,\,\,\frac{2}{{2x + 1}}\\
b)\,\,\frac{{ - 12x}}{{{x^3} - 1}}
\end{array}\)

D \(\begin{array}{l}
a)\,\,\,\frac{2}{{2x + 1}}\\
b)\,\,\frac{{ 12x}}{{{x^3} - 1}}
\end{array}\)

Câu 5 : Tìm \(P\) biết:\(\begin{align}& a)\frac{x-1}{{{x}^{2}}-x+1}-P=\frac{2}{x-1}+\frac{3x}{1-{{x}^{3}}} \\ & b)P+\frac{4x-12}{{{x}^{3}}-3{{x}^{2}}-4x+12}=\frac{3}{x-3}-\frac{{{x}^{2}}}{4-{{x}^{2}}} \\ \end{align}\)

A \(\begin{array}{l}
a)\,\,\,P = - \frac{1}{{x - 1}}\\
b)\,\,P = \frac{x}{{x + 3}}
\end{array}\)

B \(\begin{array}{l}
a)\,\,\,P = - \frac{1}{{x - 1}}\\
b)\,\,P = \frac{x}{{x - 3}}
\end{array}\)

C \(\begin{array}{l}
a)\,\,\,P = \frac{1}{{x - 1}}\\
b)\,\,P = \frac{x}{{x - 3}}
\end{array}\)

D \(\begin{array}{l}
a)\,\,\,P = \frac{1}{{x - 1}}\\
b)\,\,P = \frac{x}{{x + 3}}
\end{array}\)

Câu 6 : Tìm \(a,b,c\) sao cho\(\begin{align}& a)\frac{4x-7}{{{x}^{2}}-3x+2}=\frac{a}{x-1}+\frac{b}{x-2} \\ & b)\frac{{{x}^{2}}+5}{{{x}^{3}}-3x-2}=\frac{a}{x-2}+\frac{b}{{{(x+1)}^{2}}} \\ \end{align}\)

A \(\begin{array}{l}
a)\,\,\left\{ \begin{array}{l}
a = -3\\
b = 1
\end{array} \right.\\
b)\,\,\left\{ \begin{array}{l}
a = 1\\
b = 2
\end{array} \right.
\end{array}\)

B \(\begin{array}{l}
a)\,\,\left\{ \begin{array}{l}
a = -3\\
b = 1
\end{array} \right.\\
b)\,\,\left\{ \begin{array}{l}
a = 1\\
b = - 2
\end{array} \right.
\end{array}\)

C \(\begin{array}{l}
a)\,\,\left\{ \begin{array}{l}
a = 3\\
b = 1
\end{array} \right.\\
b)\,\,\left\{ \begin{array}{l}
a = 1\\
b = 2
\end{array} \right.
\end{array}\)

D \(\begin{array}{l}
a)\,\,\left\{ \begin{array}{l}
a = 3\\
b = 1
\end{array} \right.\\
b)\,\,\left\{ \begin{array}{l}
a = 1\\
b = - 2
\end{array} \right.
\end{array}\)

Câu 7 : Cho \(a, \, b, \, c\) thỏa mãn \(abc=2017\). Tính giá trị biểu thức sau: \[Q = \frac{{2017a}}{{ab + 2017a + 2017}} + \frac{b}{{bc + b + 2017}} + \frac{c}{{ac + 1 + c}}.\]

A \(Q=4\)

B \(Q=3\)

C \(Q=2\)

D \(Q=1\)

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