dấu / là phân số à?

a)\(\frac{x+5}{x+3}< 1\)

\(\frac{x+5}{x+3}=\frac{x+3+2}{x+3}=1+\frac{2}{x+3}\)

=> để \(\frac{x+5}{x+3}< 1\Rightarrow1+\frac{2}{x+3}< 1\Rightarrow\frac{2}{x+3}\le-1\)(đk x khác -3)

=> \(-2\le x+3< 0\)

=> x ={-5,-4}

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

để\(\frac{x+3}{x+4}>1\Rightarrow\) \(1+\frac{-1}{x+4}>1\)(đk: x khác -4)

vì \(\frac{-1}{x+4}\ne0\)

=> x+4 <0 => x<-4

p/s: dạng này chưa học ko bt đúng ko :>( cách tự chế)

\(a,B=\frac{\sqrt{x}-5}{\sqrt{x}+3}\)

Thay x=1/4 vào B ta có :

\(B=\frac{\sqrt{\frac{1}{4}}-5}{\sqrt{\frac{1}{4}+3}}=\frac{\frac{1}{2}-5}{\frac{1}{2}+3}=-\frac{9}{\frac{2}{\frac{7}{2}}}=-\frac{9}{7}\)

ĐKXĐ: x<>0; x<>1/2; x<>3; x<>-3

a: \(P=\left(\frac{6}{x^2-9}-\frac{5}{3-x}+\frac{1}{x+3}\right):\frac{2x-1}{x^2-3x}\)

\(=\left(\frac{6}{\left(x-3\right)\left(x+3\right)}+\frac{5}{x-3}+\frac{1}{x+3}\right):\frac{2x-1}{x\left(x-3\right)}\)

\(=\frac{6+5\left(x+3\right)+x-3}{\left(x-3\right)\left(x+3\right)}\cdot\frac{x\left(x-3\right)}{2x-1}\)

\(=\frac{x+3+5x+15}{x+3}\cdot\frac{x}{2x-1}=\frac{6x+18}{x+3}\cdot\frac{x}{2x-1}=\frac{6x}{2x-1}\)

b: \(P=\frac13\)

=>\(\frac{6x}{2x-1}=\frac13\)

=>18x=2x-1

=>16x=-1

=>\(x=-\frac{1}{16}\) (nhận)

c: Để P nguyên thì 6x⋮2x-1

=>6x-3+3⋮2x-1

=>3⋮2x-1

=>2x-1∈{1;-1;3;-3}

=>2x∈{2;0;4;-2}

=>x∈{1;0;2;-1}

Kết hợp ĐKXĐ, ta được: x∈{1;2;-1}

a,Ta có \(\frac{x+5}{x+3}=\frac{x+3+2}{x+3}\)\(=1+\frac{2}{x+3}\)

Để \(\frac{x+5}{x+3}< 1\)\(\Leftrightarrow1+\frac{2}{x+3}< 0\)

=>\(\frac{2}{x+3}< 0\)

=>x+3<0

=>x<-3

b, Ta có \(\frac{x+3}{x+4}=\frac{x+4-1}{x+4}=1-\frac{1}{x+4}\)

Để \(\frac{x+3}{x+4}>1\Leftrightarrow\)\(\frac{-1}{x+4}>0\)=>x+4>0=>x>-4

thank you vinamilk

a: Ta có: |x+4|=1

=>x+4=1 hoặc x+4=-1

=>x=-3(loại) hoặc x=-5

Khi x=-5 thì \(A=\dfrac{\left(-5\right)^2-5}{3\left(-5+3\right)}=\dfrac{20}{3\cdot\left(-2\right)}=\dfrac{-10}{3}\)

b: \(B=\dfrac{x-1+x+1-3+x}{\left(x-1\right)\left(x+1\right)}=\dfrac{3x-3}{\left(x-1\right)\left(x+1\right)}=\dfrac{3}{x+1}\)