Answer
$\frac{2 (100x^{2} + 95x + 11)}{(4x + 3)^{2}}$
Work Step by Step
$-8(4x+3)^{-2}+ 10(5x+1)(4x+3)^{-1}$
The greatest common factor is $(4x+3)$ with the smaller exponent in the two terms. Thus the greatest common factor is $(4x+3)^{-2}$
Express each term as the product of greatest common factor and its other factor.
$=-8(4x+3)^{-2}+ 10(5x+1)(4x+3)^{-2}(4x+3)$
$[(4x+3)^{-2}(4x+3) = (4x+3)^{-2+1} = (4x+3)^{-1} ]$
Factor out the Greatest common factor.
$=(4x+3)^{-2}(-8+10(5x+1)(4x+3))$
Multiply (5x+1) and (4x+3) using FOIL method
$= (4x+3)^{-2}(-8+10[ (5x)(4x) +(5x)(3) +(1)(4x) +(1)(3) ])$
$= (4x+3)^{-2}(-8+10[ 20x^{2} +15x + 4x + 3 ])$
$= (4x+3)^{-2}(-8+10[ 20x^{2} +19x + 3 ])$
$= (4x+3)^{-2}(-8+ 200x^{2} +190x + 30)$
$= (4x+3)^{-2}( 200x^{2} +190x + 22)$
Take out common factor 2 from $( 200x^{2} +190x + 22)$
$= (4x+3)^{-2}[2( 100x^{2} +95x + 11)]$
$= \frac{2( 100x^{2} +95x + 11)}{ (4x+3)^{2}}$ $[a^{-m} = \frac{1}{a^{m}}]$
