Question

thực hiện phép tính:

a,\(\dfrac{2x+4}{10}+\dfrac{2-x}{15}\)

b,\(\dfrac{3x}{10}+\dfrac{2x-1}{15}+\dfrac{2-x}{20}\)

c,\(\dfrac{x+1}{2x-2}+\dfrac{x^2+3}{2-2x^2}\)

d,\(\dfrac{x}{xy-y^2}+\dfrac{2x-y}{xy-x^2}\)

e,\(x+y+\dfrac{x^2+y^2}{x+y}\)

Answer 1

a: \(=\dfrac{6x+12+4-2x}{30}=\dfrac{4x+16}{30}=\dfrac{2x+8}{15}\)

b: \(=\dfrac{18x}{60}+\dfrac{8x-4}{60}+\dfrac{6-3x}{60}\)

\(=\dfrac{18x+8x-4+6-3x}{60}=\dfrac{23x+2}{60}\)

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

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

d: \(=\dfrac{x}{y\left(x-y\right)}+\dfrac{2x-y}{x\left(y-x\right)}\)

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

e: \(=\dfrac{x^2+2xy+y^2+x^2+y^2}{x+y}=\dfrac{2x^2+2xy+2y^2}{x+y}\)