5:

a: \(-120x^5y^4=20x^5y^2\cdot\left(-6y^2\right)\)

b: \(60x^6y^2=20x^5y^2\cdot3x\)

c: \(-5x^{15}y^3=20x^5y^2\cdot\left(-\dfrac{1}{4}x^{10}y\right)\)

d: \(2x^{12}y^{10}=20x^5y^2\cdot\left(\dfrac{1}{10}x^7y^8\right)\)

a: AB//CD

=>\(\dfrac{KA}{KC}=\dfrac{KB}{KD}\)

=>\(KA\cdot KD=KB\cdot KC\)

b: 

b) Ta có: \(\sqrt{150}-\sqrt{1.6}\cdot\sqrt{60}+4.5\cdot\sqrt{2\dfrac{2}{3}}-\sqrt{6}\)

\(=5\sqrt{6}-4\sqrt{6}-\sqrt{6}+\dfrac{9}{2}\cdot\sqrt{\dfrac{8}{3}}\)

\(=\dfrac{9}{2}\cdot\dfrac{2\sqrt{2}}{\sqrt{3}}\)

\(=3\sqrt{6}\)

\(\sqrt{150}+\sqrt{1,6}.\sqrt{60}+4.5\sqrt{2\dfrac{2}{3}}-\sqrt{6}\\ =5\sqrt{6}+4\sqrt{6}+3\sqrt{6}-\sqrt{6}\\ =11\sqrt{6}\)

\(\dfrac{2}{2x+1}-1\ge0\Leftrightarrow\dfrac{2}{2x+1}-\dfrac{2x+1}{2x+1}\ge0\)

\(\Leftrightarrow\dfrac{2-\left(2x+1\right)}{2x+1}\ge0\)

\(\Leftrightarrow\dfrac{1-2x}{2x+1}\ge0\)

\(\Rightarrow-\dfrac{1}{2}< x\le\dfrac{1}{2}\)

ko bt

a: \(Q=\dfrac{2x^2-4x+x-3-6}{\left(x-3\right)\left(x-2\right)}\cdot\dfrac{x-2}{x^2+1}=\dfrac{2x^2-3x-9}{x-3}\cdot\dfrac{1}{x^2+1}\)

\(=\dfrac{2x^2-6x+3x-9}{x-3}\cdot\dfrac{1}{x^2+1}=\dfrac{2x+3}{x^2+1}\)

b: Để Q>0 thì 2x+3>0

hay x>-3/2

Bài 2:

a) Q=(\(\dfrac{2x}{x-3}-\dfrac{1}{2-x}-\dfrac{6}{x^2-5x+6}\)):\(\dfrac{x^2+1}{x-2}\)

       =(\(\dfrac{2x}{x-3}+\dfrac{1}{x-2}-\dfrac{6}{x^2-2x-3x+6}\)):\(\dfrac{x^2+1}{x-2}\)

        =[\(\dfrac{2x}{x-3}+\dfrac{1}{x-2}-\dfrac{6}{x\left(x-2\right)-3\left(x-2\right)}\)]:\(\dfrac{x^2+1}{x-2}\)

        =\(\dfrac{2x\left(x-2\right)+x-3-6}{\left(x-2\right)\left(x-3\right)}\):\(\dfrac{x^2+1}{x-2}\)

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

        =\(\dfrac{2x^2-3x-9}{\left(x-2\right)\left(x-3\right)}\):\(\dfrac{x^2+1}{x-2}\)

        =\(\dfrac{2x^2-6x+3x-9}{\left(x-2\right)\left(x-3\right)}\):\(\dfrac{x^2+1}{x-2}\)

        =\(\dfrac{2x\left(x-3\right)+3\left(x-3\right)}{\left(x-2\right)\left(x-3\right)}\):\(\dfrac{x^2+1}{x-2}\)

        =\(\dfrac{\left(x-3\right)\left(2x+3\right)}{\left(x-2\right)\left(x-3\right)}\):\(\dfrac{x^2+1}{x-2}\)

        =\(\dfrac{\left(2x+3\right)}{\left(x-2\right)}\):\(\dfrac{x^2+1}{x-2}\)

         =\(\dfrac{2x+3}{x^2+1}\)

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

\(\dfrac{b^2+b}{a+ab}=\dfrac{b\left(b+1\right)}{a\left(b+1\right)}=\dfrac{b}{a}\)

d) Để phân thức \(\dfrac{4x^3+4x^2}{x^2-1}\) có nghĩa thì: \(x^2-1\ne0\Leftrightarrow x\ne\pm1\)

Khi đó: \(\dfrac{4x^3+4x^2}{x^2-1}=\dfrac{4x^2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{4x^2}{x-1}\)

e) Để phân thức \(\dfrac{b^2+b}{a+ab}\) có nghĩa thì: \(a+ab\ne0\Leftrightarrow a\ne-ab\)

Khi đó: \(\dfrac{b^2+b}{a+ab}=\dfrac{b\left(b+1\right)}{a\left(1+b\right)}=\dfrac{b}{a}\)

a) Để phương trình có nghiệm thì: m²≠0 =>m≠0

b) Vì phương trình có nghiệm bằng -2m

=>-(m+2)2m-m²=0 ⇔-2m²-4m-m²=0 ⇔-3m²-4m=0 ⇔-m(3m+4)=0 

⇔m=0 hay m=\(\dfrac{-4}{3}\)mà m phải khác 0 nên m=\(\dfrac{-4}{3}\).

c) -(m+2)x-m²=0 ⇔x=\(\dfrac{m^2}{m+2}\)>0 ⇔m+2>0 ⇔m>-2.

d)  -(m+2)x-m²=0 ⇔x=\(\dfrac{m^2}{m+2}\).

Để x nguyên thì m² ⋮ m+2.

⇔ m²-4+4 ⋮ m+2

⇔ 4 ⋮ m+2

⇔ m∈{-1;-3;0;-4;2;-6} mà m khác 0 nên m∈{-1;-3;-4;2;-6}

em ăn nhiều bánh nhất

em ăn \(\dfrac{1}{2}=\dfrac{3}{6}\) cái bánh

chị ăn \(\dfrac{2}{3}=\dfrac{4}{6}\) cái bánh

⇒chị ăn nhiều bánh hơn

(cách mình trình bày chắc chắn là không đúng nên bạn trình bày lại theo cách cô chỉ nha!)

a: Xét ΔKAB và ΔKCD có

\(\widehat{KAB}=\widehat{KCD}\)(hai góc so le trong, AB//CD)

\(\widehat{AKB}=\widehat{CKD}\)(hai góc đối đỉnh)

Do đó: ΔKAB đồng dạng với ΔKCD

=>\(\dfrac{KA}{KC}=\dfrac{KB}{KD}\)

=>\(KA\cdot KD=KB\cdot KC\)

b: Ta có: \(\dfrac{KA}{KC}=\dfrac{KB}{KD}\)

=>\(\dfrac{KC}{KA}=\dfrac{KD}{KB}\)

=>\(\dfrac{KC}{KA}+1=\dfrac{KD}{KB}+1\)

=>\(\dfrac{KC+KA}{KA}=\dfrac{KD+KB}{KB}\)

=>\(\dfrac{AC}{KA}=\dfrac{BD}{KB}\)

=>\(\dfrac{AK}{AC}=\dfrac{BK}{BD}\left(1\right)\)

Xét ΔADC có IK//DC

nên \(\dfrac{AK}{AC}=\dfrac{IK}{DC}\left(2\right)\)

Xét ΔBDC có KQ//DC

nên \(\dfrac{KQ}{DC}=\dfrac{BK}{BD}\left(3\right)\)

Từ (1),(2),(3) suy ra IK=KQ