Question

Thực hiện phép tính:

a) \(\frac{1}{x}-\frac{1}{x+1}\)

b)\(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}\)

c) \(\frac{9x-3}{4x-1}-\frac{3x}{1-4x}\)

d) \(\frac{2x-1}{x}-\frac{2x+5}{3x-4x^2}+\frac{2x^2+x+3}{3x-4x^2}\)

e) \(\frac{x}{2x+1}+\frac{1}{4x^2-1}-\frac{x-2}{2x-1}\)

giúp mình với mình cần gấp ! Help me ===)

Answer 1

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

b, \(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}=\frac{y^2-xy-xy+x^2}{\left(xy-x^2\right)\left(y^2-xy\right)}=\frac{x^2+y^2}{xy^3-xyxy-xyxy+x^3y}\)Tu rut gon tiep

c, tt

d, cx r

Answer 2

a) \(\frac{1}{x}-\frac{1}{x+1}=\frac{x+1}{x\left(x+1\right)}-\frac{x}{x\left(x+1\right)}\)

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

b) \(\frac{1}{xy-x^2}-\frac{1}{y^2-xy}=\frac{1}{x\left(y-x\right)}-\frac{1}{y\left(y-x\right)}\)

\(=\frac{y}{xy\left(y-x\right)}-\frac{x}{xy\left(y-x\right)}=\frac{y-x}{xy\left(y-x\right)}=\frac{1}{xy}\)

c) \(\frac{9x-3}{4x-1}-\frac{3x}{1-4x}=\frac{9x-3}{4x-1}+\frac{3x}{4x-1}\)

\(=\frac{9x-3+3x}{4x-1}=\frac{6x-3}{4x-1}\)

Answer 3

\(a,\frac{1}{x}-\frac{1}{x+1}\)

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

\(=\frac{1}{x\left(x+1\right)}\)

\(b,\frac{1}{xy-x^2}-\frac{1}{y^2-xy}\)

\(=\frac{1}{x\left(y-x\right)}-\frac{1}{y\left(y-x\right)}\)

\(=\frac{y}{xy\left(y-x\right)}-\frac{x}{xy\left(y-x\right)}=\frac{x-y}{xy\left(x-y\right)}=\frac{1}{xy}\)

Answer 4

\(\frac{x}{2x+1}+\frac{1}{4x^2-1}-\frac{x-2}{2x-1}=\frac{x}{2x+1}+\frac{1}{\left(2x+1\right)\left(2x-1\right)}-\frac{x-2}{2x-1}=\)

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

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

Câu e là câu này nhe

Answer 5

d) \(\frac{2x-1}{x}-\frac{2x+5}{3x-4x^2}+\frac{2x^2+x+3}{3x-4x^2}\)

\(=\frac{\left(2x-1\right)\left(3-4x\right)}{x\left(3-4x\right)}-\frac{2x+5}{x\left(3-4x\right)}+\frac{2x^2+x+3}{x\left(3-4x\right)}\)

\(=\frac{-8x^2+10x-3-2x-5+2x^2+x+3}{x\left(3-4x\right)}\)

\(=\frac{-6x^2+9x-5}{x\left(3-4x\right)}\)

Answer 6

e) \(\frac{x}{2x+1}+\frac{1}{4x^2-1}-\frac{x-2}{2x-1}\)

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

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

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