\(9^{x-1}=9\)

\(x-1=1\)

\(x=2\)

d.\(x^2-4x-x^2+8=0\)

\(-4x=-8\)

\(x=2\)

c. \(6x^2-\left(6x^2-4x+15x-10\right)=7\)

\(6x^2-6x^2-11x+10=7\)

\(-11x=-3\)

\(x=\frac{3}{11}\)

b. \(21x-15x^2-35+25x-\left(10x-15x^2+4-6x\right)=4\)

\(-15x^2+46x-35-10x+15x^2-4+6x=4\)

\(42x-39=4\)

\(42x=42\)

\(x=1\)

a. \(x\left(x^2-25\right)-\left(x^3-2x^2+4x+2x^2-4x+8\right)=17\)

\(x^3-25x-\left(x^3+8\right)=17\)

\(x^3-25x-x^3-8=17\)

\(-25x=25\)

\(x=-1\)

\(\left[\begin{array}{nghiempt}\hept{\begin{cases}x-3>0\\x+5< 0\end{array}\right.\\\hept{\begin{cases}x-3< 0\\x+5>0\end{array}\right.\end{array}\right.\)

\(\left[\begin{array}{nghiempt}\hept{\begin{cases}x>3\\x< -5\end{array}\right.\\\hept{\begin{cases}x< 3\\x>-5\end{array}\right.\end{array}\right.\)

loại trg hợp x<3 và x>-5

=> -5<x<3 thì \(\frac{x-3}{x+5}< 0\)

b.\(\frac{7}{3}+x-\frac{3}{2}=\frac{3}{2}x\)

\(\frac{5}{6}+x=\frac{3}{2}x\)

\(-\frac{1}{2}x=\frac{-5}{6}\)

\(x=\frac{5}{3}\)

\(B=-9x^2+6x-5\)

\(B=-9\left(x^2-\frac{2}{3}x+\frac{5}{9}\right)\)

\(B=-9\left(x^2-\frac{2}{3}x+\frac{1}{9}+\frac{4}{9}\right)\)

\(B=-9\left(x-\frac{1}{3}\right)^2-4\)

Vì \(-9\left(x-\frac{1}{3}\right)^2< 0\)  với mọi x 

=>\(B=-9\left(x-\frac{1}{3}\right)^2-4< -4\)  với mọi x 

B max=-4 khi x=1/3 

hay B luôn âm

\(2x^2+3\left(x^2-1\right)=5x^2-5x\)

\(2x^2+3x^2-3=5x^2-5x\)

\(5x^2-3=5x^2-5x\)

\(5x=3\)

\(x=\frac{3}{5}\)

c.\(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right).230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{7}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)

\(\frac{\frac{25}{108}.\frac{5751}{25}+\frac{187}{4}}{\frac{100}{21}:-\frac{41}{21}}\)

\(\frac{\frac{213}{4}+\frac{187}{4}}{-\frac{100}{41}}\)

\(\frac{100}{-\frac{100}{41}}=-41\)