Réponse :
Explications étape par étape :
1)
[tex]A(x)=4(2x+5)^{2} -(x+1)(3-x)\\A(x)= 4(4x^{2} +20x+25)-(3x-x^{2} +3-x)=16x^{2} +80x+100-3x+x^{2} -3+x\\A(x)= 17x^{2} +74x+97[/tex]
2a)
[tex]B(x)= 225x^{2} +9+90x=225x^{2} +90x+9=(15x+3)^{2}[/tex]
2b)
[tex]C(x)=(1-3x)^{2} -(4x+7)^{2} =(1-3x+4x+7)(1-3x-4x-7)=(x+8)(-7x-6)[/tex]
3a)
[tex]D(x)=\frac{2}{x+3} +4=\frac{2}{x+3}+\frac{4*(x+3)}{x+3} =\frac{2+4x+12}{x+3} =\frac{4x+14}{x+3} \\\\[/tex]
3b)
[tex]E(x)=\frac{4}{x-4} -\frac{3x}{x+1} =\frac{4*(x+1)}{(x-4)(x+1)} -\frac{3x*(x-4)}{(x+1)(x-4)} =\frac{(4x+4)-(3x^{2} -12x)}{(x+1)(x-4)} =\frac{4x+4-3x^{2} +12x}{(x+1)(x-4)\\}\\ E(x) =\frac{-3x^{2}+16x+4 }{(x+1)(x-4)}[/tex]
