2.3 Product and quotient rules; question 55

[Eigenvalue]

Differentiate the function

g(x)=([tex]\frac{x+1}{x+2}[/tex])(2x-5)

[Eigenvalue]

g'(x)=(2x-5)'([tex]\frac{x+1}{x+2}[/tex])+([tex]\frac{x+1}{x+2}[/tex])'(2x-5)

=2([tex]\frac{x+1}{x+2}[/tex])+([tex]\frac{x+2-(x+1)}{(x+2)²}[/tex])(2x-5)

=[tex]\frac{2x+2}{x+2}[/tex]+[tex]\frac{2x-5}{(x+2)²}[/tex]

=[tex]\frac{(2x+2)(x+2)+2x-5}{(x+2)²}[/tex]

=[tex]\frac{2x²+8x-1}{x²+4x+4}[/tex]