Ta có :\(\text{VT = A + B}\)

\(\text{= ( a + b + 5 ) + ( b – c – 9 )}\)

\(\text{= a + b + 5 + b – c – 9}\)

\(\text{= a + ( b + b ) – c + ( 5 – 9 )}\)

\(\text{= a + 2b – c – 4 (1)}\)

\(\text{VP = C – D}\)

\(\text{= ( b – c – 4 ) – ( -b – a )}\)

\(\text{= b – c – 4 + b + a}\)

\(\text{= ( b + b ) – c + a – 4}\)

\(\text{= 2b – c + a – 4}\)

\(\text{= a + 2b – c – 4 (2)}\)

\(\text{từ (1) và (2) suy ra}\)\(\text{ A + B = C – D ( đpcm ) }\)

a: \(\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{a-b}{c-d}\)

1: Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)

=>\(a=b\cdot k;c=d\cdot k\)

\(\dfrac{a}{a+b}=\dfrac{bk}{bk+b}=\dfrac{bk}{b\left(k+1\right)}=\dfrac{k}{k+1}\)

\(\dfrac{c}{c+d}=\dfrac{dk}{dk+d}=\dfrac{dk}{d\left(k+1\right)}=\dfrac{k}{k+1}\)

Do đó: \(\dfrac{a}{a+b}=\dfrac{c}{c+d}\)

2: \(\dfrac{2a+b}{a-2b}=\dfrac{2\cdot bk+b}{bk-2b}=\dfrac{b\left(2k+1\right)}{b\left(k-2\right)}=\dfrac{2k+1}{k-2}\)

\(\dfrac{2c+d}{c-2d}=\dfrac{2dk+d}{dk-2d}=\dfrac{d\left(2k+1\right)}{d\left(k-2\right)}=\dfrac{2k+1}{k-2}\)

Do đó: \(\dfrac{2a+b}{a-2b}=\dfrac{2c+d}{c-2d}\)

3: \(\dfrac{a+b}{a-b}=\dfrac{bk+b}{bk-b}=\dfrac{b\left(k+1\right)}{b\cdot\left(k-1\right)}=\dfrac{k+1}{k-1}\)

\(\dfrac{c+d}{c-d}=\dfrac{dk+d}{dk-d}=\dfrac{d\left(k+1\right)}{d\left(k-1\right)}=\dfrac{k+1}{k-1}\)

Do đó: \(\dfrac{a+b}{a-b}=\dfrac{c+d}{c-d}\)

4: \(\dfrac{5a+3b}{5c+3d}=\dfrac{5\cdot bk+3b}{5dk+3d}=\dfrac{b\left(5k+3\right)}{d\left(5k+3\right)}=\dfrac{b}{d}\)

\(\dfrac{5a-3b}{5c-3d}=\dfrac{5\cdot bk-3b}{5\cdot dk-3d}=\dfrac{b\left(5k-3\right)}{d\left(5k-3\right)}=\dfrac{b}{d}\)

Do đó: \(\dfrac{5a+3b}{5c+3d}=\dfrac{5a-3b}{5c-3d}\)

\(\text{#TNam}\)

`a,` \(\text{Xét Tam giác ABD và Tam giác AED có:}\)

`AB = AE (g``t)`

\(\widehat{BAD}=\widehat{EAD} (\text {tia phân giác} \) \(\widehat{BAE})\)

`\text {AD chung}`

`=> \text {Tam giác ABD = Tam giác AED (c-g-c)}`

`b,`

\(\text{Vì Tam giác ABD = Tam giác AED (a)}\)

`->`\(\widehat{ADB}=\widehat{ADE} (\text {2 góc tương ứng})\)

`-> \text {AD là tia phân giác}` \(\widehat{BDE}\)

\(\text{Xét Tam giác ABC:}\)

`AC > AB (g``t)`

\(\text{Theo định lý của quan hệ giữa góc và cạnh đối diện trong 1 tam giác}\)

`->`\(\widehat{ABC}>\widehat{ACB}.\) 

* Xét A+B= a+b-5+(-b)-c+1

= a+[ b+(-b)]+(-5+1)-c

= a-4-c (1)

* Xét C-D=b-c-4-(b-a)

=b-c-4-b+a

=b-b+a-c-4

=a-c-4 (2)

Từ (1) và (2)

\(\Rightarrow A+B=C-D\)

ta có : A + B = a + b - 5 - b - c + 1 = a - c - 4 (1)

C - D = b - c - 4 - (b - a) = b - c - 4 - b + a = a - c - 4 = (1)

vậy A + B = C - D (đpcm)

\(A=a+b-5\)

\(B=-b-c+1\)

\(C=b-c-4\)

\(D=b-a\)

\(A+B=(a+b-5)+(-b-c+1)\)

\(A+B=a+b-5-b-c+1=a-4-c\)

\(C-D=(b-c-4)-(b-a)\)

\(C-D=b-c-4-b+a=c-4+a\)

\(C-D=A+B(đpcm)\)

(mk cx ko chắc lắm)

có A + B = (a + b - 5 )+( b -c  +1 )

A + B = a + b - 5 + b -c +1

= a + ( b +  b ) -c - 5 +1

= a + 2b -c -4

Có  C - D = b-c-4-(b-a)

=b-c-4-b+a

=a+2b-c-4

K nha

A+B=a+b-5+(-b-c+1)=a+b-5+(-b)-c+1=a-c-4

C-D=b-c-4-(b-a)=b-c-4-b+a=a-c-4

Vậy A+B=C-D