7,Thực hiện phép tính
a,\(\frac{4x+1}{2}-\frac{3x+2}{3}\)
b,\(\frac{x+3}{x}-\frac{x}{x-3}+\frac{9}{x^2-3x}\)
c,\(\frac{x+3}{x^2-1}-\frac{1}{x^2+x}\)
d,\(\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{-10x+8}{9x^2-4}\)
e,\(\frac{3x}{5x+5y}-\frac{x}{10x-10y}\)
f,\(\frac{3}{2x^2+2x}+\frac{2x-1}{x^2-1}-\frac{2}{x}\)
a: \(=\dfrac{12x+3-6x-4}{6}=\dfrac{6x-1}{6}\)
b: \(=\dfrac{x^2-9-x^2+9}{x\left(x-3\right)}=0\)
c: \(=\dfrac{x\left(x+3\right)-x+1}{x\left(x+1\right)\left(x-1\right)}=\dfrac{x^2+2x+1}{x\left(x+1\right)\left(x-1\right)}=\dfrac{x+1}{x\left(x-1\right)}\)
d: \(=\dfrac{3x+2-12x+8+10x-8}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{x+2}{\left(3x-2\right)\left(3x+2\right)}\)
e: \(=\dfrac{6x\left(x-y\right)-x\left(x+y\right)}{10\left(x+y\right)\left(x-y\right)}\)
\(=\dfrac{6x^2-6xy-x^2-xy}{10\left(x+y\right)\left(x-y\right)}=\dfrac{5x^2-7xy}{10\left(x+y\right)\left(x-y\right)}\)
f: \(=\dfrac{3}{2x\left(x+1\right)}+\dfrac{2x-1}{\left(x+1\right)\left(x-1\right)}-\dfrac{2}{x}\)
\(=\dfrac{3x-3+4x^2-2x-4x^2+4}{4x\left(x+1\right)\left(x-1\right)}=\dfrac{x+1}{4x\left(x+1\right)\left(x-1\right)}=\dfrac{1}{4x\left(x-1\right)}\)
