Bài 5:
a: \(\dfrac{x^2+3x}{x-4}:P=\dfrac{x^2-9}{x^2-4x}\)
=>\(\dfrac{x\left(x+3\right)}{x-4}:P=\dfrac{\left(x-3\right)\left(x+3\right)}{x\left(x-4\right)}\)
=>\(P=\dfrac{x\left(x+3\right)}{x-4}:\dfrac{\left(x-3\right)\left(x+3\right)}{x\left(x-4\right)}\)
=>\(P=\dfrac{x\left(x+3\right)}{x-4}\cdot\dfrac{x\left(x-4\right)}{\left(x-3\right)\left(x+3\right)}\)
=>\(P=\dfrac{x^2}{x-3}\)
b: \(Q:\dfrac{x-2}{2x+3}=\dfrac{4x^2+12x+9}{x^2-4}\)
=>\(Q:\dfrac{x-2}{2x+3}=\dfrac{\left(2x+3\right)^2}{\left(x-2\right)\left(x+2\right)}\)
=>\(Q=\dfrac{\left(2x+3\right)^2}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x-2}{2x+3}=\dfrac{2x+3}{x+2}\)
Bài 6:
a: \(\dfrac{1-x^2}{x^2+2x}:\dfrac{2-2x}{3x}\)
\(=\dfrac{\left(1-x\right)\left(1+x\right)}{x\left(x+2\right)}\cdot\dfrac{3x}{2\left(1-x\right)}\)
\(=\dfrac{3}{x+2}\cdot\dfrac{1+x}{2}=\dfrac{3x+3}{2x+4}\)
b: \(\dfrac{x^3+1}{x-1}:\left(x^2-x+1\right)\)
\(=\dfrac{x^3+1}{\left(x-1\right)\left(x^2-x+1\right)}\)
\(=\dfrac{\left(x+1\right)\left(x^2-x+1\right)}{\left(x-1\right)\left(x^2-x+1\right)}=\dfrac{x+1}{x-1}\)
c: \(\dfrac{x^2-x-2}{x^2+3x+2}:\dfrac{x^2-4x+4}{x^2+2x}\)
\(=\dfrac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}:\dfrac{\left(x-2\right)^2}{x\left(x+2\right)}\)
\(=\dfrac{x-2}{x+2}\cdot\dfrac{x\left(x+2\right)}{\left(x-2\right)^2}=\dfrac{x}{x-2}\)
Bài 3:
= x^2 - 3^2/ 2x + 6/ x - 3
= ( x + 3 ) ( x - 3 )/ 2x + 6/ x - 3
= ( x + 3 ) ( x - 3 )/ 2( x + 3 )/ x - 3
= x + 3/ 2 ( x + 3 )
= 1/2
dấu "/" là phân số bạn nhé!
