Question

E(x) = (x+5 supra x+4 minus x-7 supra xla puterea2 +3x-4): x+2supra x-1

Answer 1

E(x) =[ (x+5)/(x+4) - (x-7)/(x²+3x-4)]: (x+2)/(x-1)=
= [(x+5)/(x+4) - (x-7)/(x²+3x-4)] ×(x-1)/ (x+2)=
= [(x+5)/(x+4) - (x-7)/(x²+4x-x-4)] ×(x-1)/ (x+2)=
= [(x+5)(x-1)-x+7)/(x+4)(x-1)] ×(x-1)/ (x+2)=
= [(x²+5x-x-5-x+7)/(x+4)(x-1)] ×(x-1)/ (x+2)=
=(x²+3x+2)/(x+4)× 1/ (x+2)=
=(x²+2x+x+2)/(x+4)× 1/ (x+2)=
=(x+2)(x+1)/(x+4)× 1/ (x+2)=
=(x+1)/(x+4)