Answer:
1. [tex]\frac{x^2+4x-7}{x-1}[/tex]
2. [tex]\frac{x^2-2x+7}{x-1}[/tex]
3. [tex]\frac{2x^2-x-7}{x-1}[/tex]
4. [tex]\frac{2x^2-3x+7}{x-1}[/tex]
Step-by-step explanation:
1. [tex](x+5) + \frac{-2}{x-1}[/tex]
Taking LCM
[tex]=\frac{(x-1)(x+5)+(-2)}{x-1}\\ Solving:\\=frac{x(x+5)-1(x+5)-2}{x-1} \\=frac{x^2+5x-1x-5-2}{x-1} \\Adding\,\,like\,\,terms:\\=\frac{x^2+4x-7}{x-1}[/tex]
2. [tex]x-1 +\frac{6}{x-1}[/tex]
Taking LCM and solving
[tex]=\frac{(x-1)(x-1)+6}{x-1}\\=\frac{(x(x-1)-1(x-1)+6}{x-1}\\=\frac{x^2-1x-1x+1+6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{x^2-2x+7}{x-1}[/tex]
3. [tex](2x+1)+\frac{-6}{x-1}[/tex]
Taking LCM and solving:
[tex]=\frac{(2x+1)(x-1)-6}{x-1} \\=\frac{2x(x-1)+1(x-1)-6}{x-1} \\=\frac{2x^2-2x+1x-1-6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{2x^2-x-7}{x-1}[/tex]
4. [tex](2x-1)+\frac{6}{x-1}[/tex]
Taking LCM and solving:
[tex]=\frac{(2x-1)(x-1)+6}{x-1} \\=\frac{2x(x-1)-1(x-1)-6}{x-1} \\=\frac{2x^2-2x-1x+1+6}{x-1}\\Adding\,\,like\,\,terms:\\=\frac{2x^2-3x+7}{x-1}[/tex]
