Bài 5:
a: \(\dfrac{-1}{2-3x}+\dfrac{5}{3x-2}\)
\(=\dfrac{1}{3x-2}+\dfrac{5}{3x-2}\)
\(=\dfrac{1+5}{3x-2}=\dfrac{6}{3x-2}\)
b: \(\dfrac{2a-1}{2a+1}-\dfrac{2a-3}{2a-1}\)
\(=\dfrac{\left(2a-1\right)^2-\left(2a-3\right)\left(2a+1\right)}{\left(2a+1\right)\left(2a-1\right)}\)
\(=\dfrac{4a^2-4a+1-\left(4a^2+2a-6a-3\right)}{\left(2a+1\right)\left(2a-1\right)}\)
\(=\dfrac{4a^2-4a+1-4a^2+4a+3}{\left(2a+1\right)\left(2a-1\right)}=\dfrac{4}{4a^2-1}\)
c: \(\dfrac{2}{x+3}+\dfrac{3}{x^2-9}\)
\(=\dfrac{2}{x+3}+\dfrac{3}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{2\left(x-3\right)+3}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{2x-3}{\left(x-3\right)\left(x+3\right)}\)
Bài 6:
a: \(\dfrac{1}{x+1}-\dfrac{1}{x-1}-\dfrac{2x^2}{1-x^2}\)
\(=\dfrac{1}{x+1}-\dfrac{1}{x-1}+\dfrac{2x^2}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{x-1-x-1+2x^2}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{2x^2-2}{x^2-1}=2\)
b: \(\dfrac{x+1}{\left(x+2\right)^2}-\dfrac{1}{x+2}-\dfrac{1}{1-x^2}\)
\(=\dfrac{x+1}{\left(x+2\right)^2}-\dfrac{1}{x+2}+\dfrac{1}{\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{\left(x+1\right)\left(x^2-1\right)-\left(x+2\right)\left(x^2-1\right)+\left(x+2\right)^2}{\left(x-1\right)\left(x+1\right)\left(x+2\right)^2}\)
\(=\dfrac{x^3-x+x^2-1-x^3+x-2x^2+2+\left(x+2\right)^2}{\left(x-1\right)\left(x+1\right)\left(x+2\right)^2}\)
\(=\dfrac{\left(x+2\right)^2-x^2+1}{\left(x-1\right)\left(x+1\right)\left(x+2\right)^2}\)
\(=\dfrac{4x+5}{\left(x-1\right)\left(x+1\right)\left(x+2\right)^2}\)
c: \(x^2+\dfrac{x^4+1}{1-x^2}+1\)
\(=\dfrac{\left(x^2+1\right)\left(1-x^2\right)+x^4+1}{1-x^2}\)
\(=\dfrac{1-x^4+x^4+1}{1-x^2}=\dfrac{2}{1-x^2}\)
