3/ Ta có:

\(A=\dfrac{1-2x}{x+3}\)

\(A=\dfrac{-2x+1}{x+3}\)

\(A=\dfrac{-2x-6+7}{x+3}\)

\(A=\dfrac{-2\left(x+3\right)+7}{x+3}\)

\(A=-2+\dfrac{7}{x+3}\)

A nguyên khi \(\dfrac{7}{x+3}\) nguyên 

⇒ 7 ⋮ \(x+3\)

\(\Rightarrow x+3\inƯ\left(7\right)\)

\(\Rightarrow x+3\in\left\{1;-1;7;-7\right\}\)

\(\Rightarrow x\in\left\{-2;-4;4;-10\right\}\)

Để A nguyên thì x^2 chia hết cho x+1

=>x^2-1+1 chia hết cho x+1

=>\(x+1\in\left\{1;-1\right\}\)

=>\(x\in\left\{0;-2\right\}\)

a: ĐểA nguyên thì x^2+2x+x+2-3 chia hết cho x+2

=>-3 chia hết cho x+2

=>x+2 thuộc {1;-1;3;-3}

=>x thuộc {-1;-3;1;-5}

b: B nguyên khi x^2+x+3 chia hết cho x+1

=>3 chia hết cho x+1

=>x+1 thuộc {1;-1;3;-3}

=>x thuộc {0;-2;2;-4}

a) Ta có: \(A=\left(\dfrac{x-5\sqrt{x}}{x-25}-1\right):\left(\dfrac{25-x}{x+2\sqrt{x}-15}-\dfrac{\sqrt{x}+3}{\sqrt{x}+5}+\dfrac{\sqrt{x}-5}{\sqrt{x}-3}\right)\)

\(=\left(\dfrac{\sqrt{x}\left(\sqrt{x}-5\right)}{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}-1\right):\left(\dfrac{25-x}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}-\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}+\dfrac{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}\right)\)

\(=\left(\dfrac{\sqrt{x}}{\sqrt{x}+5}-1\right):\left(\dfrac{25-x-\left(x-9\right)+x-25}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}\right)\)

\(=\left(\dfrac{\sqrt{x}}{\sqrt{x}+5}-\dfrac{\sqrt{x}+5}{\sqrt{x}+5}\right):\left(\dfrac{25-x-x+9+x-25}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}\right)\)

\(=\dfrac{\sqrt{x}-\sqrt{x}-5}{\sqrt{x}+5}:\dfrac{x+9}{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{-5}{\sqrt{x}+5}\cdot\dfrac{\left(\sqrt{x}+5\right)\left(\sqrt{x}-3\right)}{x+9}\)

\(=\dfrac{-5\left(\sqrt{x}-3\right)}{x+9}\)

THAM KHẢO

\(P=\dfrac{x-5}{x-4}:\dfrac{x-5}{2x}=\dfrac{2x}{x-4}\)

\(\Rightarrow\)\(\dfrac{2x}{x-4}\in Z\)

\(\Rightarrow\)\(\dfrac{2\left(x-4\right)+8}{x-4}\in Z\)

\(\Rightarrow\)\(2+\dfrac{8}{x-4}\in Z\Rightarrow\)\(\dfrac{8}{x-4}\in Z\Rightarrow x-4\inƯ\left(8\right)=\left\{...\right\}\)

Bạn làm tiếp nhé!

\(a,P=\dfrac{2x^2+2x+2+2x-1+x^2+6x+2}{\left(x-1\right)\left(x^2+x+1\right)}\\ P=\dfrac{3x^2+10x+3}{\left(x-1\right)\left(x^2+x+1\right)}\)

Bài 1:

x/-3=9/4

nên x=-9/4*3=-27/4

2x+y=-4

=>y=-4-2x=-4-2*(-27/4)=-4+27/2=27/2-8/2=19/2

help

Để C là số nguyên thì x chia hết cho 2x-1

=>2x chia hết cho 2x-1

=>2x-1+1 chia hết cho 2x-1

=>\(2x-1\in\left\{1;-1\right\}\)

mà x lớn nhất

nên 2x-1=1

=>x=1