Đề không hiển thị hai biểu thức A và B. Bạn xem lại nhé.

a: Khi x=5 thì A=5/(5+3)=5/8

b: \(C=A+B=\dfrac{x}{x+3}+\dfrac{2}{x-3}+\dfrac{3-5x}{x^2-9}\)

\(=\dfrac{x^2-3x+2x+6+3-5x}{\left(x-3\right)\left(x+3\right)}=\dfrac{x^2-6x+9}{\left(x-3\right)\left(x+3\right)}=\dfrac{x-3}{x+3}\)

c: Để C nguyên thì x+3-6 chia hết cho x+3

=>\(x+3\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

=>\(x\in\left\{-2;-4;-1;-5;0;-6;-9\right\}\)

Bài 2: 

Ta có: \(P=\dfrac{15\sqrt{x}-11}{x+2\sqrt{x}-3}-\dfrac{3\sqrt{x}-2}{\sqrt{x}-1}-\dfrac{2\sqrt{x}+3}{\sqrt{x}+3}\)

\(=\dfrac{15\sqrt{x}-11-3x-9\sqrt{x}+2\sqrt{x}+6-2x+2\sqrt{x}-3\sqrt{x}+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)

\(=\dfrac{-5x+7\sqrt{x}-2}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)

\(=\dfrac{-5\sqrt{x}+1}{\sqrt{x}+3}\)

a: |2x-3|=1

=>2x-3=1 hoặc 2x-3=-1

=>x=1(nhận) hoặc x=2(loại)

KHi x=1 thì \(A=\dfrac{1+1^2}{2-1}=2\)

b: ĐKXĐ: x<>-1; x<>2

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

\(A=x^2-x+5=2^2-2+5=2+5=7\)

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

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

\(=-2\)

\(a,đk\left(B\right):x\ne\pm3\\ B=\dfrac{3}{x-3}-\dfrac{6x}{9-x^2}+\dfrac{x}{x+3}\\ =\dfrac{3}{x-3}+\dfrac{6x}{x^2-9}+\dfrac{x}{x+3}\\ =\dfrac{3\left(x+3\right)+6x+x\left(x-3\right)}{x^2-9}\\ =\dfrac{3x+9+6x+x^2-3x}{x^2-9}\\ =\dfrac{x^2+6x+9}{x^2-9}\\ =\dfrac{\left(x+3\right)^2}{x^2-9}\\ =\dfrac{x+3}{x-3}\)

\(b,P=A.B\\ =\dfrac{x+1}{x+3}\times\dfrac{x+3}{x-3}\\ =\dfrac{x+1}{x-3}\)

\(c,\) Để P nguyên 

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

=> \(x-3\inƯ\left(4\right)\)

\(Ư\left(4\right)=\left\{-1;1;2;-2;4;-4\right\}\)

\(=>x=\left\{2;4;5;1;7;-1\right\}\)

Ta có:B=(x-1/x+2)+(2-5x/4-x^2)

            =[(x-1)*(x-2)/(x+2)-(2-5x)/(x-2)*(x+2)]

            =(x^2+2x)/(x-2)*(x+2)

            =x/(x-2)

=> 5B=5x/(x-2)

=>A-5B = (x^3+2/x-2)-(5x/x-2)=x^3-5x+2/x-2=(x-2)*(x^2+2x-1)/(x-2)=x^2+2x-1=(x+1)^2-2

vì (x+1)^2>= 0

=> A-5B= (x+1)^2-2>= -2

Dấu `=' xảu ra<=> (x+1)^2 =0

=>x=-1

vậy GTNN của P=-2 <=> x=-1

a. Thay a = 14, b = 15, c = 10, ta có:

\(a=a\times b+200\)

\(=>a=14\times15+200\)

\(=>a=210+200=410\)

___

\(b=a\times b\times c\)

\(=>b=14\times15\times10=2100\)

b. Vì 410 < 2100 nên a < b.

\(#NqHahh\)

a: Khi a=14 và b=15 thì \(A=14\cdot15+200=210+200=410\)

Khi a=14 và b=15 và c=10 thì \(B=14\cdot15\cdot10=210\cdot10=2100\)

b: A=410

B=2100

=>A<B