x ×2 + x × 3 = 4
Giai ho mk
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\(\frac{x}{3}=\frac{y}{2}\Rightarrow\frac{x}{15}=\frac{y}{10}\) (1)
\(\frac{y}{5}=\frac{z}{3}\Rightarrow\frac{y}{10}=\frac{z}{6}\) (2)
Từ (1) và (2) \(\Rightarrow\frac{x}{15}=\frac{y}{10}=\frac{z}{6}\)
Và x + y + z = 46
Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
\(\frac{x}{15}=\frac{y}{10}=\frac{z}{6}=\frac{x+y+z}{15+10+6}=\frac{46}{31}\)
Ta có:
\(\frac{x}{15}=\frac{46}{31}\Rightarrow x=\frac{46}{31}.15=\frac{690}{31}\)
\(\frac{y}{10}=\frac{46}{31}\Rightarrow y=\frac{46}{31}.10=\frac{460}{31}\)
\(\frac{z}{6}=\frac{46}{31}\Rightarrow z=\frac{46}{31}.6=\frac{276}{31}\)
Vậy \(x=\frac{690}{31};y=\frac{460}{31};z=\frac{276}{31}\)
\(\frac{4}{x+2}+\frac{-3}{x-2}+\frac{12}{x^2-4}.\)
\(=\frac{4\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}-\frac{3\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}+\frac{12}{\left(x+2\right)\left(x-2\right)}\)
\(=\frac{4x-8-3x-6+12}{\left(x-2\right)\left(x+2\right)}\)
\(=\frac{x-4}{x^2-4}\)
\(\frac{4}{x+2}+\frac{\left(-2\right)}{x-2}+\frac{12}{x^2-4}\)
\(=\frac{4\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}-\frac{3\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\frac{12}{\left(x+2\right)\left(x-2\right)}\)
\(=\frac{4\left(x-2\right)-3\left(x+2\right)+12}{\left(x+2\right)\left(x-2\right)}\)
\(=\frac{x-2}{\left(x+2\right)\left(x-2\right)}\)
\(=\frac{1}{x+2}\)
( x + 2 ) ( x + 3 ) ( x + 4 ) ( x + 5 ) - 24
= ( x2 + 7x + 10 ) ( x2 + 7x + 12 ) - 24
Đặt x2 + 7x + 10 = y
Ta có :
y2 + 2y - 24 = ( y - 4 ) ( y + 6 ) = ( x2 + 7x + 6 ) ( x2 + 7x + 16 )
= ( x + 1 ) ( x + 6 ) ( x2 + 7x + 16 )
Đặt x2+7x+10=t
\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left[\left(x+2\right)\left(x+5\right)\right]\left[\left(x+3\right)\left(x+4\right)\right]\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24=t\left(t+2\right)-24=t^2+2t-24\)
\(=\left(t^2+2t+1\right)-25=\left(t+1\right)^2-5^2=\left(t-4\right)\left(t+6\right)\)=(x2+7x+6)(x2+7x+16)
=(x2+x+6x+6)(x2+7x+16)=[x(x+1)+6(x+1)](x2+7x+16)=(x+1)(x+6)(x2+7x+16)
x×2+x×3=4
x×(2+3)=4
x×5=4
4 khong chia het cho 5
x.2+x.3=4
x.(2+3) =4
x.5 =4
x =4:5
x =0,8
=> x=0,8