Question

Докажите тождество :(5x/x-10+20x/x2-20x+100):4x-24/x2-100-25xx-10=5x4

Answer 1

1)5x/(x-10)+20x/(x-10)²=(5x²-50x+20x)/(x-10)²=(5x²-30x)/(x-10)²=
=5x(x-6)/(x-10)²
2)5x/(x-10)² *(x-10)(x+10)/4(x-6)=(5x²+50x)/4(x-10)
3)(5x²+50x)/4(x-10)-25/(x-10)=(5x²+50x-100x)/4(x-10)=
=(5x²-50x)/4(x-10)=5x(x-10)/4(x-10)=5x/4