by Thực hiện phép tính:
a) \(\left( x-3 \right)\left( x-6 \right)+x\left( 4-x \right)\)
b) \(\frac{5x}{x-1}+\frac{3x-8}{x-1}\) \(\)
c) \({{\left( x+4 \right)}^{2}}-25+\left( 3+x \right)\left( 3-x \right)\)
d) \(\frac{2x-1}{x}+\frac{2x+5}{4x-3}+\frac{2{{x}^{2}}+x+3}{3x-4{{x}^{2}}}\)
A. \(a) -5x+18. \) \( b) 8. \)
\( c) 8x. \) \(d) 2 \)
B. \(a) -5x+18. \) \( b) 8. \)
\( c) 9x. \) \(d) 2 \)
C. \(a) -5x+18. \) \( b) 8. \)
\( c) 8x. \) \(d) 10 \)
D. \(a) -5x_18. \) \( b) 8x. \)
\( c) 8x-1. \) \(d) 2 \)
Hướng dẫn Chọn đáp án là: A
Phương pháp giải:
– Nhân phá ngoặc hoặc qui đồng rồi rút gọn.
Lời giải chi tiết:
\(\begin{align} & a)\,\,\left( x-3 \right)\left( x-6 \right)+x\left( 4-x \right) \\ & ={{x}^{2}}-6x-3x+18+4x-{{x}^{2}} \\ & =-5x+18. \\\end{align}\) \(\begin{align} & c)\,\,{{\left( x+4 \right)}^{2}}-25+\left( 3+x \right)\left( 3-x \right) \\ & ={{x}^{2}}+8x+16-25+9-{{x}^{2}} \\ & =8x. \\\end{align}\)
\(\begin{align} & b)\,\,\frac{5x}{x-1}+\frac{3x-8}{x-1}\ \ \ \left( DK:\ \ x\ne 1 \right) \\ & =\frac{5x+3x-8}{x-1} \\ & =\frac{8x-8}{x-1} \\ & =\frac{8\left( x-1 \right)}{x-1}=8. \\\end{align}\) \(\begin{align} & d)\,\,\frac{2x-1}{x}+\frac{2x+5}{4x-3}+\frac{2{{x}^{2}}+x+3}{3x-4{{x}^{2}}}\ \ \ \ \left( Dk:\ \ x\ne 0,\ \ x\ne \frac{3}{4} \right) \\ & =\frac{\left( 2x-1 \right)\left( 3-4x \right)-x\left( 2x+5 \right)+\left( 2{{x}^{2}}+x+3 \right)}{x\left( 3-4x \right)} \\ & =\frac{6x-8{{x}^{2}}-3+4x-2{{x}^{2}}-5x+2{{x}^{2}}+x+3}{x\left( 3-4x \right)} \\ & =\frac{-8{{\text{x}}^{2}}+6\text{x}}{\text{x}\left( 3-4\text{x} \right)} \\ & =\frac{\text{2}x\left( -4x+3 \right)}{x\left( 3-4x \right)}=2 \\\end{align}\)
Chọn A
