48:
a: \(\dfrac{6x^2+13x-5}{2x+5}\)
\(=\dfrac{6x^2+15x-2x-5}{2x+5}\)
\(=\dfrac{3x\left(2x+5\right)-\left(2x+5\right)}{2x+5}=3x-1\)
b: \(\dfrac{x^3-3x^2+x-3}{x-3}\)
\(=\dfrac{x^2\left(x-3\right)+\left(x-3\right)}{x-3}=x^2+1\)
c: \(\dfrac{2x^4+x^3-5x^2-3x-3}{x^2-3}\)
\(=\dfrac{2x^4-6x^2+x^2-3+x^3-3x}{x^2-3}\)
\(=\dfrac{2x^2\left(x^2-3\right)+\left(x^2-3\right)+x\left(x^2-3\right)}{x^2-3}\)
\(=2x^2+x+1\)
Bài 49:
a: \(\dfrac{\left(12x^2-14x+3-6x^3+x^4\right)}{1-4x+x^2}\)
\(=\dfrac{x^4-6x^3+12x^2-14x+3}{x^2-4x+1}\)
\(=\dfrac{x^4-4x^3+x^2-2x^3+8x^2-2x+3x^2-12x+3}{x^2-4x+1}\)
\(=x^2-2x+3\)
b: \(\dfrac{x^5-x^2-3x^4+3x+5x^3-5}{5+x^2-3x}\)
\(=\dfrac{x^5-3x^4+5x^3-x^2+3x-5}{x^2-3x+5}\)
\(=\dfrac{x^3\left(x^2-3x+5\right)-\left(x^2-3x+5\right)}{x^2-3x+5}=x^3-1\)
c: \(\dfrac{2x^2-5x^3+2x+2x^4-1}{x^2-x-1}\)
\(=\dfrac{2x^4-5x^3+2x^2+2x-1}{x^2-x-1}\)
\(=\dfrac{2x^4-2x^3-2x^2-3x^3+3x^2+3x+x^2-x-1}{x^2-x-1}\)
\(=2x^2-3x+1\)
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giúp mình với ạ,mình xin cảm ơn trước