Question

giúp mik vs

 

Answer 1

4: \(\frac{5}{x-2}=\frac{5\cdot\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}=\frac{5x+10}{\left(x-2\right)\left(x+2\right)}\)

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

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

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

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

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

7: \(\frac{2}{x^2-6x+9}=\frac{2}{\left(x-3\right)^2}=\frac{2\left(x+3\right)}{\left(x-3\right)^2\cdot\left(x+3\right)}=\frac{2x+6}{\left(x+3\right)\left(x-3\right)^2}\)

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

8: \(\frac{1-x}{5x-10}=\frac{1-x}{5\left(x-2\right)}=\frac{x\left(1-x\right)}{5x\left(x-2\right)}=\frac{x-x^2}{5x\left(x-2\right)}\)

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

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

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

10: \(\frac{1-2x}{x^2-3x}=\frac{1-2x}{x\left(x-3\right)};\frac{3}{3-x}=\frac{-3}{x-3}=\frac{-3x}{x\left(x-3\right)}\)

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

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

12: \(\frac{7x-1}{2x^3-18x}=\frac{7x-1}{2x\left(x^2-9\right)}=\frac{7x-1}{2x\left(x-3\right)\left(x+3\right)}\)

\(\frac{5x-3}{x^2-9}=\frac{5x-3}{\left(x-3\right)\left(x+3\right)}=\frac{2x\left(5x-3\right)}{2x\left(x-3\right)\left(x+3\right)}=\frac{10x^2-6x}{2x\left(x-3\right)\left(x+3\right)}\)

13: \(\frac{1-2x}{x^2+x+1}=\frac{1-2x}{x^2+x+1}\)

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