what are the solutions to the equation $\frac{w}{2w - 3}=\frac{4}{w}$?\n$w=-6$ and $w = - 2$\n$w = 0,w = 2$…

what are the solutions to the equation $\frac{w}{2w - 3}=\frac{4}{w}$?\n$w=-6$ and $w = - 2$\n$w = 0,w = 2$, and $w = 6$\n$w = 0$ and $w=\frac{3}{2}$\n$w = 2$ and $w = 6$

what are the solutions to the equation $\frac{w}{2w - 3}=\frac{4}{w}$?\n$w=-6$ and $w = - 2$\n$w = 0,w = 2$, and $w = 6$\n$w = 0$ and $w=\frac{3}{2}$\n$w = 2$ and $w = 6$

Answer

Answer:

D. $w = 2$ and $w = 6$

Explanation:

Step1: Cross - multiply

$w\times w=4\times(2w - 3)$ $w^{2}=8w - 12$

Step2: Rearrange to quadratic form

$w^{2}-8w + 12 = 0$

Step3: Factor the quadratic

$(w - 2)(w - 6)=0$

Step4: Solve for w

$w-2 = 0$ gives $w = 2$; $w - 6=0$ gives $w = 6$