Question

\(\dfrac{450}{x+30}\)-\(\dfrac{450}{x}\)=4

Answer 1

\(\dfrac{450}{x+30}-\dfrac{450}{x}=4\left(đk:x\ne0,x\ne-30\right)\)

\(\Leftrightarrow\dfrac{450x-450x-13500}{x\left(x+30\right)}=4\)

\(\Leftrightarrow\dfrac{-13500}{x\left(x+30\right)}=4\)

\(\Leftrightarrow4x^2+120x=-13500\)

\(\Leftrightarrow4\left(x+15\right)^2=-12600\)

\(\Leftrightarrow\left(x+15\right)^2=-3150\)(vô lý)

Vậy \(x\in\varnothing\)

Answer 2

\(\dfrac{450}{x+30}-\dfrac{450}{x}=4\)

<=> \(\dfrac{450x}{x\left(x+30\right)}-\dfrac{450\left(x+30\right)}{x\left(x+30\right)}=\dfrac{4x\left(x+30\right)}{x\left(x+30\right)}\)

<=> 450x - 450(x + 30) = 4x(x + 30)

<=> 450x - 450x - 480 = 4x² + 120x

<=> 4x² - 120x - 480 = 0

<=> x = 33, 57

Answer 3

Ta có: \(\dfrac{450}{x+30}-\dfrac{450}{x}=4\)

\(\Leftrightarrow4x\left(x+30\right)=450x-450\left(x+30\right)\)

\(\Leftrightarrow4x^2+120x+13500=0\)(vô lý)