1（2sinx+3cosx）/（4sinx-9cosx)
=(2tanx+3)/(4tanx-9) (分子分母同时除以cosx,sinx/cosx=tanx)
=(4+3)/(8-9)=-7
2 (2sin²x-3cos²x)/(4sin²x+9cos²x) (分子分母同时除以cos²x,sin²x/cos²x=tan²x)
=(2tan²x-3)/(4tan²x+9)
=(8-3)/(16+9)=1/5
3 4sin²x-3sinx*cosx-5cos²x
=(4sin²x-3sinx*cosx-5cos²x)/(sin²x+cos²x) (sin²x+cos²x=1)
=(4tan²x-3tanx-5)/(tan²x+1)
=(8-6-5)/(4+1)=-3/5
4 (sinx-cos^5x)/(3sin³x-cos³x） (sin²x+cos²x)^2=sin⁴x+cos⁴x+2sin²xcos²x=1
=[sinx(sin⁴x+cos⁴x+2sin²xcos²x)-cos^5x]/[(3sin³x-cos³x)(sin²x+cos²x]
=[sin^5x+sinxcos⁴x+2sin³xcos²x)-cos^5x]/[(3sin³x-cos³x)(sin²x+cos²x]
=(tan^5x+tanx+2tan³x-1)/[(3tan³x-1)(tan²x+1)]
=(32+2+16-1)/[(24-1)(4+1)]=49/115
5 23/(3sin³xcosx-cos⁴x)
=23（sin⁴x+cos⁴x+2sin²xcos²x)/(3sin³xcosx-cos⁴x)
=23(tan⁴x+1+2tan²x)/(3tan³x-1)
=23(16+1+8)/(24-1)
=25