Bài tập:
Cho biểu thức=(3a+3b+5c)-(-3a+2b+4c)
Rút gọn biểu thức
Cần gấp.
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a) 3a + 4b - 5c - 2a - 3b + 5c
= ( 3a - 2a ) + ( 4b - 3b ) - ( 5c - 5c )
= a + b
b) 7a + 3b - 4c - 3a + 2b - 2c - 4a + b - 2c
= ( 7a - 3a - 4a ) + ( 3b + 2b + b ) - ( 4c + 2c + 2c )
= 6b - 8c
a) 3a + 4b - 5c - 2a - 3b + 5c
= (3a - 2a) + (4b - 3b) - (5c - 5c)
= a + b - 0 = a + b
b) 7a + 3b - 4c - 3a + 2b - 2c - 4a + b - 2c
= (7a - 3a - 4a) + (3b + 2b + b) - ( 4c + 2c + 2c)
= 0 + 6b - 8c = 6b - 8c
\(\frac{3a-2b}{5}=\frac{2c-5a}{3}=\frac{5b-3c}{2}=\frac{15a-10b}{25}=\frac{6c-15a}{9}=\frac{10b-6c}{4}\)
\(=\frac{15a-10b+6c-15a+10b-6c}{25+9+4}=0\)
\(\Rightarrow\left\{{}\begin{matrix}3a=2b\\2c=5a\\5b=3c\end{matrix}\right.\Rightarrow\frac{a}{2}=\frac{b}{3}=\frac{c}{5}=\frac{a+b+c}{10}\)
\(\Rightarrow\left\{{}\begin{matrix}a=\frac{a+b+c}{5}\\b=\frac{3\left(a+b+c\right)}{10}\\c=\frac{a+b+c}{2}\end{matrix}\right.\)
\(\Rightarrow P=\frac{\frac{33\left(a+b+c\right)}{10}}{\frac{43\left(a+b+c\right)}{10}}=\frac{33}{43}\)
a) (3a-2b+c)-(2a+b)-(c-a)
= 3a - 2b + c - 2a - b - c + a
= 3a - 2b - b + c - c - 2a + a
= 3a - (2b + b) + (c - c) - (2a - a)
= 3a - 3b + 0 - a
= 3a - a - 3b
= 2a - 3b
b) (a-b)-(b+c)-(c+a)
= a - b - b - c - c - a
= a - a - b - b - c - c
= ( a - a) - ( b + b) - ( c + c)
= 0 - 2b - 2c
b) (a-b)-(b+c)-(c+a)
= a - b - b - c -c - a
= (a - a ) - ( b + b ) - ( c + c )
= 0 - 2b - 2c
= -2b - 2c
= -(2b + 2c)
= -2(b+c)
a) M = 8ab;
b) N = [ ( 3 a + + 2 ) + ( 1 – 2 b ) ] 2 = ( 3 a – 2 b + 3 ) 2 .
A = (-2a + 3b - 4c) - (-2a - 3b - 4c)
= -2a + 3b - 4c +2a + 3b + 4c
=6b
Bài 1: Đặt \(\dfrac{a}{c}=\dfrac{b}{d}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=ck\\b=dk\end{matrix}\right.\)
\(\dfrac{a}{a+c}=\dfrac{ck}{ck+c}=\dfrac{ck}{c\left(k+1\right)}=\dfrac{k}{k+1}\)
\(\dfrac{b}{b+d}=\dfrac{dk}{dk+d}=\dfrac{k}{k+1}\)
Do đó: \(\dfrac{a}{a+c}=\dfrac{b}{b+d}\)
\(\left(3a+3b+5c\right)-\left(-3a+2b+4c\right).\)
\(=3a+3b+5c+3a-2b-4c\)
\(=6a+b+c\)