Question

a shares transaction summary shows a total cost of $2,400 before fees. if the share price had been $2 cheaper, the investor could have purchased 200 more shares. simplify and factor the equation \\(\frac{2,400}{x - 2} - \frac{2,400}{x} = 200\\) to find the price per share of the stock. round to the nearest hundredth if necessary.

Explanation:

Step1: Factor out common term

Factor $\frac{2400}{x(x-2)}$ from left side.
$\frac{2400x - 2400(x-2)}{x(x-2)} = 200$

Step2: Simplify numerator

Expand and simplify the numerator.
$\frac{2400x -2400x +4800}{x(x-2)} = 200$
$\frac{4800}{x(x-2)} = 200$

Step3: Eliminate denominator

Multiply both sides by $x(x-2)$.
$4800 = 200x(x-2)$

Step4: Divide by 200

Simplify the equation by dividing.
$24 = x(x-2)$

Step5: Rearrange to quadratic form

Expand and rearrange to standard quadratic.
$x^2 -2x -24 = 0$

Step6: Factor quadratic

Factor the quadratic expression.
$(x-6)(x+4) = 0$

Step7: Solve for x

Find valid positive solution (price can't be negative).
$x=6$ or $x=-4$; discard $x=-4$

Answer:

$\$6.00$