\(\dfrac{\sqrt{x}}{\sqrt{x}-1}\)+\(\dfrac{4}{\sqrt{x}\left(\sqrt{x}-1\right)}\)x\(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\)

=\(\dfrac{\sqrt{x}}{\sqrt{x}-1}\)+​​\(\dfrac{4}{\sqrt{x}\left(\sqrt{x}+1\right)}\)​​

=\(\dfrac{\sqrt{x}\cdot\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)+\(\dfrac{4\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

=\(\dfrac{x}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)+\(\dfrac{4\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

=\(\dfrac{x+4\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

Còn lại tự làm đê :))) công nhận ai ra đề mà ác vc

a: \(B=\frac{\tan\alpha-\cot\alpha}{cos\alpha-\sin\alpha}=\left(\frac{\sin\alpha}{cos\alpha}-\frac{cos\alpha}{\sin\alpha}\right):\left(cos\alpha-\sin\alpha\right)\)

\(=\frac{\sin^2\alpha-cos^2\alpha}{\sin\alpha\cdot cos\alpha\cdot\left(cos\alpha-\sin\alpha\right)}=\frac{\sin\alpha+cos\alpha}{\sin\alpha\cdot cos\alpha}\)

\(\tan\alpha=2\)

=>\(\sin\alpha=2\cdot cos\alpha\)

\(B=\frac{\sin\alpha+cos\alpha}{\sin\alpha\cdot cos\alpha}=\frac{2\cdot cos\alpha+cos\alpha}{2\cdot cos\alpha\cdot cos\alpha}=\frac{3\cdot cos\alpha}{2\cdot cos^2\alpha}=\frac{3}{2\cdot cos^2\alpha}\)

Ta có: \(1+\tan^2\alpha=\frac{1}{cos^2\alpha}\)

=>\(\frac{1}{cos^2\alpha}=1+2^2=5\)

=>\(B=\frac32\cdot5=\frac{15}{2}\)

Xét ΔMNP vuông tại M có MH là đường cao

nên \(MH^2=HN\cdot HP\)

=>\(HN\cdot HP=4,8^2=23,04\)
HN+HP=PN(H nằm giữa N và P)

=>HN+HP=10

mà \(HN\cdot HP=23,04\)

nên HN,HP là các nghiệm của phương trình:

\(A^2-10A+23,04=0\)

=>(A-3,6)(A-6,4)=0

=>A=3,6 hoặc A=6,4

Vậy: Sẽ có 2 trường hợp:

HN=3,6cm và HP=6,4cm

hoặc HN=6,4cm và HP=3,6cm

giải giúp tui!!Please!!

Cai nay lop 7 ma, Ap dung cong thuc tinh canh huyen tam giac vuong la ra duong cheo cua cac tam giac trong hinh thang

told - didn't believe 

will pass

is wearing 

had left 

has been typing 

came - was washing 

decided - am going to invite

will tell

are going to go - will have 

are you going to learn 

was playing - was reading 

finish

has just arrived - is waiting - will come 

went - had left 

Have you decided - will go

will you home => will you come 

leaves => will leave 

eats => ate 

have => will have 

went => was going 

amazing => amazed

wears => is wearing 

is rising => rises 

don't => didn't 

studied => was studying 

enjoy => enjoyed 

played => play 

did you do => were you doing 

am => have been 

eat => ate

\(x^2\sqrt{9-x^2}\)

Ta có:

\(9-x^2\le9\forall x\)

\(Minx^2\sqrt{9-x^2}=0\Leftrightarrow x=0\)

- Gọi O là giao điểm của AC và BD.

- AB//CD nên góc BAC = góc ACD (so le trong), tương tự góc ABD=góc BDC.

- Theo đề bài góc ACD=gócBDC nên góc BAC=góc ABD.

=>Tam giác ABO cân tại O

=> 0A=0B.(1)

Tương tự tam giác ODC cân tại O

=>OD=OC.(2)

Lại có góc AOD=góc BOC (đối đỉnh )

(3) Từ (1), (2), (3) suy ra tam giác AOD = tam giác OBC

nên suy ra :

=> AD = BC