a, ĐKXĐ:\(\left\{{}\begin{matrix}x^2-1\ne0\\x+1\ne0\\x-1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\pm1\\x\ne-1\\x\ne1\end{matrix}\right.\Leftrightarrow x\ne\pm1\)

b, \(P=\dfrac{2x^2}{x^2-1}+\dfrac{x}{x+1}-\dfrac{x}{x-1}\)

\(\Rightarrow P=\dfrac{2x^2}{\left(x+1\right)\left(x-1\right)}+\dfrac{x\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}-\dfrac{x\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}\)

\(\Rightarrow P=\dfrac{2x^2}{\left(x+1\right)\left(x-1\right)}+\dfrac{x^2-x}{\left(x+1\right)\left(x-1\right)}-\dfrac{x^2+x}{\left(x+1\right)\left(x-1\right)}\)

\(\Rightarrow P=\dfrac{2x^2+x^2-x-x^2-x}{\left(x+1\right)\left(x-1\right)}\)

\(\Rightarrow P=\dfrac{2x^2-2x}{\left(x+1\right)\left(x-1\right)}\)

\(\Rightarrow P=\dfrac{2x\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}\)

\(\Rightarrow P=\dfrac{2x}{x+1}\)

c, Thay x=2 vào P ta có:

\(P=\dfrac{2x}{x+1}=\dfrac{2.2}{2+1}=\dfrac{4}{3}\)

\(P=\dfrac{-1}{1.2}+\dfrac{-1}{2.3}+...+\dfrac{-1}{199.200}\\ =-1\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{199.200}\right)\\ =-1\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{199}-\dfrac{1}{200}\right)\)

Rồi tự giải tiếp

\(a,\dfrac{5}{4}+\dfrac{7}{3}=\dfrac{15}{12}+\dfrac{28}{12}=\dfrac{43}{12}\\ b,\dfrac{4}{5}\times\dfrac{5}{8}=\dfrac{4}{8}=\dfrac{1}{2}\\ c,\dfrac{2}{3}-\dfrac{3}{8}=\dfrac{16}{24}-\dfrac{9}{24}=\dfrac{7}{24}\\ d,\dfrac{5}{6}:\dfrac{1}{3}=\dfrac{5}{6}\times\dfrac{1}{3}=\dfrac{5}{18}\)

cần giải à ?

\(\Delta'=\left[-\left(m+3\right)\right]^2-\left(m^2+3\right)=m^2+6m+9-m^2-3=6m+6\)

Để pt có nghiệm thì \(\Delta'\ge0\Leftrightarrow6m+6\ge0\Leftrightarrow m\ge-1\)

Khi đó x₁ + x₂ = -2(m+3), x₁ . x₂ = m²+3

\(2x^2-3=-2\dfrac{1}{2}\\ \Rightarrow2x^2=\dfrac{1}{2}\\ \Rightarrow x^2=\dfrac{1}{4}\\ \Rightarrow x=\pm\dfrac{1}{2}\)

Chiều cao mảnh đất là:

12x`(2)/(3)`=8(m)

Diện tích mảnh đất là:

12x8=96(m²)

Đáp số: 96m²

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