Question

Thực hiện phép tính.

a.( x²-x)/xy +(1-4x)/xy

b. (5xy²-x²y)/3xy + (4xy² +xy²)/ 3xy

c.(x+1)/ab+ (x-1)/b-a

d. (2x+4)/10+ (2-x)/15

e. (x+1)/ (2x-2)+ (x²+3)/ (2-2x²)

f. (1-2x)/2x+ 2x/ (2x-1)+ 1/ (2x-4x²)

g. x²/ (x²-4x)+ 6/ (6-3x)+ 1/(x+2)

Answer 1

a: \(=\dfrac{x^2-x+1-4x}{xy}=\dfrac{x^2-5x+1}{xy}\)

b: \(=\dfrac{5xy^2-x^2y+4xy^2+xy^2}{3xy}\)

\(=\dfrac{10xy^2-x^2y}{3xy}=\dfrac{xy\left(10y-x\right)}{3xy}=\dfrac{10y-x}{3}\)

d: \(\dfrac{2x+4}{10}-\dfrac{2-x}{15}\)

\(=\dfrac{x+2}{5}+\dfrac{x-2}{15}\)

\(=\dfrac{3x+6+x-2}{15}=\dfrac{4x+4}{15}\)

e: \(=\dfrac{x+1}{2\left(x-1\right)}-\dfrac{x^2+3}{2\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{x^2+2x+1-x^2-3}{2\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{2\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x+1}\)