Bài 5:
a/\(\dfrac{3x^2-2x}{x-3}+\dfrac{4x+1}{3-x}+\dfrac{10-2x^2}{x-3}\)
\(=\dfrac{3x^2-2x}{x-3}-\dfrac{4x+1}{x-3}+\dfrac{10-2x^2}{x-3}\)
\(=\dfrac{3x^2-2x-4x-1+10-2x^2}{x-3}\)
\(=\dfrac{x^2-6x+9}{x-3}=\dfrac{\left(x-3\right)^2}{x-3}=x-3\)
b/\(\dfrac{2-a^2}{a-2}+\dfrac{a-2a^2}{2-a}+\dfrac{2-3a}{a-2}\)
\(=\dfrac{2-a^2}{a-2}-\dfrac{a-2a^2}{a-2}+\dfrac{2-3a}{a-2}\)
\(=\dfrac{2-a^2-a+2a^2+2-3a}{a-2}\)
\(=\dfrac{a^2-4a+4}{a-2}=\dfrac{\left(a-2\right)^2}{a-2}=a-2\)
c/\(\dfrac{x+37}{x-5}-\dfrac{12+10x}{x-5}-\dfrac{x\left(x-1\right)}{5-x}\)
\(=\dfrac{x+37}{x-5}-\dfrac{12+10x}{x-5}+\dfrac{x^2-x}{x-5}\)
\(=\dfrac{x+37-12-10x+x^2-x}{x-5}\)
\(=\dfrac{x^2-10x+25}{x-5}=\dfrac{\left(x-5\right)^2}{x-5}=x-5\)
Bài 6:
a: \(\dfrac{5}{x+3}+\dfrac{7-2x}{x^2-9}\)
\(=\dfrac{5}{x+3}+\dfrac{7-2x}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{5\left(x-3\right)+7-2x}{\left(x+3\right)\left(x-3\right)}\)
\(=\dfrac{3x-8}{\left(x+3\right)\left(x-3\right)}\)
b: \(\dfrac{x}{3y^2-xy}+\dfrac{9y}{x^2-3xy}\)
\(=\dfrac{x}{y\left(3y-x\right)}+\dfrac{9y}{x\left(x-3y\right)}\)
\(=\dfrac{-x}{y\left(x-3y\right)}+\dfrac{9y}{x\left(x-3y\right)}\)
\(=\dfrac{-x^2+9y^2}{xy\left(x-3y\right)}\)
\(=-\dfrac{\left(x-3y\right)\left(x+3y\right)}{xy\left(x-3y\right)}=\dfrac{-x-3y}{xy}\)
c: \(\dfrac{3}{x-2}-\dfrac{8-x}{2x-4}\)
\(=\dfrac{3}{x-2}+\dfrac{x-8}{2\left(x-2\right)}\)
\(=\dfrac{6+x-8}{2\left(x-2\right)}=\dfrac{x-2}{2\left(x-2\right)}=\dfrac{1}{2}\)
d: \(\dfrac{2x+9}{9-4x^2}-\dfrac{1}{2x+3}\)
\(=\dfrac{-2x-9}{\left(2x-3\right)\left(2x+3\right)}-\dfrac{1}{2x+3}\)
\(=\dfrac{-2x-9-2x+3}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{-4x-6}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{-2}{2x-3}\)
