化简求值:(x^2-16)/(x^2+8x+16)+x/(x-4)+1/(x^2-16),其中x=(根号下2)+1
1个回答

(x^2-16)/(x^2+8x+16)+x/(x-4)+1/(x^2-16)

=(x+4)(x-4))/(x+4)^2+x/(x-4)+1/[(x+4)(x-4)]

=(x-4))/(x+4)+x/(x-4)+1/[(x+4)(x-4)]

=[(x-4)^2+x(x+4)+1]/[(x+4)(x-4)]

=(2x^2-4x+17)/(x^2-16)

=[2(x-1)^2+15]/(x^2-16)

x=√2+1

x-1=(√2+1)-1=√2

x^2=(√2+1)^2=3+2√2

(x^2-16)/(x^2+8x+16)+x/(x-4)+1/(x^2-16)

=[2(√2)^2+15]/(3+2√2-16)

=19/(2√2-13)

=19*(2√2+13)/[(2√2-13)*(2√2+13)]

=-(38√2+247)/161