Oh, học tới BĐT luôn

\(x\left(x-3\right)-x^2+9=0\Leftrightarrow x\left(x-3\right)-\left(x^2-9\right)=0\Leftrightarrow x\left(x-3\right)-\left(x+3\right)\left(x-3\right)=0\Leftrightarrow\left(x-x+3\right)\left(x-3\right)=0\Leftrightarrow3\left(x-3\right)=0=>x=3\)

\(\frac{2a}{a-1}+\frac{a}{1-a}=\frac{2a}{a-1}+\frac{-a}{a-1}=\frac{2a-a}{a-1}=\frac{a}{a-1}\)

\(\frac{5x+3}{x+2}+\frac{7}{x+2}=\frac{5x+3+7}{x+2}=\frac{5x+10}{x+2}=\frac{5\left(x+2\right)}{x+2}=5\)

Đề này thì 10Đ khỏe

Xét vế trái:

A = 1+2+2²+2³+....+2¹⁰⁰

2A = 2+2²+2³+2⁴+....+2¹⁰¹

2A - A = 2¹⁰¹ - 1

=> A = 2¹⁰¹ - 1 = vế phải

=> 1+2+2²+2³+....+2¹⁰⁰ = 2¹⁰¹ - 1 (đpcm)

\(x^2+2x+1-y^2=\left(x^2+2x+1\right)-y^2=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)

x²-y²+3x+3y=(x+y)(x-y)+3(x+y)=(x+y)(x-y-3)

đề căng quá! dài đây