a) P(x) - Q(x)

\(=\left(\right.x^3-3x^2+x+1\left.\right)-\left(\right.2x^3-x^2+3x-4\left.\right)\)

\(= x^{3} - 3 x^{2} + x + 1 - 2 x^{3} + x^{2} - 3 x + 4\)

\(= - x^{3} - 2 x^{2} - 2 x + 5\).

Vậy P(x) - Q(x)= \(-x^3-2x^2-2x+5\)

b) Thay \(x = 1\) vào hai đa thức ta có:

\(P\left(\right.1\left.\right)=1^3-3.1^2+1+1=0\)

\(Q\left(\right.1\left.\right)=2.1^3-1^2+3.1-4=0\)

Vậy \(x = 1\) là nghiệm của cả hai đa thức \(P \left(\right. x \left.\right)\) và \(Q \left(\right. x \left.\right)\).

a) \(\frac{x}{- 4} = \frac{- 11}{2}\)

\(x=\left\lbrack\left(-11\right).\left(-4\right)]:2\right.\)

\(x = 22\).

b) \(\frac{15 - x}{x + 9}=\frac{3}{5}\)

\(\left(\right.15-x\left.\right).5=\left(\right.x+9\left.\right).3\)

\(75-5x=3x+27\)

\(8 x = 48\)

\(x = 6\).