a: \(\dfrac{3x^2+5xy-2y^2}{3x^2-7xy+2y^2}\)
\(=\dfrac{3x^2+6xy-xy-2y^2}{3x^2-6xy-xy+2y^2}\)
\(=\dfrac{3x\left(x+2y\right)-y\left(x+2y\right)}{3x\left(x-2y\right)-y\left(x-2y\right)}\)
\(=\dfrac{\left(x+2y\right)\left(3x-y\right)}{\left(x-2y\right)\left(3x-y\right)}=\dfrac{x+2y}{x-2y}\)
b: Ta có: \(\dfrac{a^4-5a^2+4}{a^4-a^2+4a-4}\)
\(=\dfrac{a^4-a^2-4a^2+4}{a^2\left(a^2-1\right)+4\left(a-1\right)}\)
\(=\dfrac{a^2\left(a^2-1\right)-4\left(a^2-1\right)}{a^2\left(a-1\right)\left(a+1\right)+4\left(a-1\right)}\)
\(=\dfrac{\left(a-1\right)\left(a+1\right)\left(a-2\right)\left(a+2\right)}{\left(a-1\right)\left(a^3+a^2+4\right)}\)
\(=\dfrac{\left(a+1\right)\left(a-2\right)\left(a+2\right)}{a^3+a^2+4}\)
\(=\dfrac{\left(a+1\right)\left(a-2\right)\left(a+2\right)}{a^3+2a^2-a^2+4}\)
\(=\dfrac{\left(a+1\right)\left(a-2\right)\left(a+2\right)}{a^2\left(a+2\right)-\left(a+2\right)\left(a-2\right)}\)
\(=\dfrac{\left(a+1\right)\left(a-2\right)\left(a+2\right)}{\left(a+2\right)\left(a^2-a+2\right)}\)
\(=\dfrac{a^2-a-2}{a^2-a+2}\)
