3(x+3) - x² + 9

= 3(x +3) - ( x² - 9 )

=3(x+3) - (x² - 3²)

= 3(x + 3) - (x - 3)(x+3)

= (x+3)(3 - x + 3)

= x(x+3)

Chúc học tốt^^

\(f\left(x\right)=\left(x-2\right)\left(x-3\right)Q\left(x\right)+ax+b\) (Q(x) là thương, ax + b là số dư)

f (x) chia cho x - 2 dư 3 tức f(2) = 3 \(\Rightarrow2a+b=3\) (1)

f(x) chia x - 3 dư 4 tức f(3) = 4 \(\Rightarrow3a+b=4\) (2)

Từ (1) và (2), ta được \(3a+b-\left(2a+b\right)=4-3=1\Rightarrow a=1\Rightarrow b=1\)

Vậy đa thức dư là ax + b = x + 1

cảm ơn bạn nhiều lắm 

\(\frac{x^2+y^2}{xy}=\frac{25}{12}\Rightarrow12\left(x^2+y^2\right)=25xy\)

\(\Rightarrow12x^2+12y^2-25xy=0\Rightarrow12x\left(x-2y\right)-y\left(x-2y\right)=0\Rightarrow\left(12x-y\right)\left(x-2y\right)=0\)

\(x< y< 0\Rightarrow12x< y\Rightarrow12x-y< 0\)

Do đó: \(x-2y=0\Rightarrow x=2y\)

Vậy \(A=\frac{x-y}{x+y}=\frac{2y-y}{2y+y}=\frac{1}{3}\)

\(\left(a-b\right)=11\Rightarrow\left(a-b\right)^2=121\Rightarrow a^2-2ab+b^2=121\)

\(145-2ab=121\)

\(\Rightarrow2ab=145-121=24\)

\(\Rightarrow ab=12\)

\(\Rightarrow a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)=11.\left(145+12\right)=11.157\)

Ta có: \(a-b=11\)

\(\Rightarrow\left(a-b\right)^2=11^2\)

\(a^2-2ab+b^2=121\)

Lại có: \(a^2+b^2=145\)

\(\Rightarrow145-2ab=121\)

\(\Rightarrow2ab=145-121\)

\(2ab=24\)

\(\Rightarrow ab=12\)

\(a^3-b^3\)

\(=\left(a-b\right)\left(a^2+ab+b^2\right)\)

\(=11.\left(145+12\right)\)

\(=11.157\)

\(=1727\)

\(\frac{4}{x-1}-\frac{2}{1-x}-\frac{x}{x-1}\)

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

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

ĐKXĐ: \(x\ne1\)

\(\frac{4}{x-1}-\frac{2}{1-x}-\frac{x}{x-1}\)

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

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

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

a) \(\frac{6xy+4y}{4x^2y^2}+\frac{2xy-4y}{4x^2y^2}\)

\(=\frac{6xy+4y+2xy-4y}{4x^2y^2}\)

\(=\frac{8xy}{4x^2y^2}\)

\(=\frac{2}{xy}\)

b) \(\frac{5}{x+3}-\frac{3}{x-3}+\frac{30}{x^2-9}\)

\(=\frac{5\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}-\frac{3\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}+\frac{30}{\left(x-3\right)\left(x+3\right)}\)

\(=\frac{5x-15-3x-9+30}{\left(x+3\right)\left(x-3\right)}\)

\(=\frac{2x+6}{\left(x+3\right)\left(x-3\right)}\)

\(=\frac{2\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}\)

\(=\frac{2}{x-3}\)

c) \(\frac{2x+8}{\left(x+2\right)^2}:\frac{x+4}{x+2}\)

\(=\frac{2\left(x+4\right)}{\left(x+2\right)^2}\cdot\frac{x+2}{x+4}\)

\(=\frac{2\left(x+4\right)\left(x+2\right)}{\left(x+2\right)\left(x+2\right)\left(x+4\right)}\)

\(=\frac{2}{x+2}\)