Solve 200/x-200/(x + 5)=2

Question

Solve the equation

x_{1} = - 25, x_{2} = 20

Evaluate

\frac{200}{x} - \frac{200}{x + 5} = 2

Find the domain

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\frac{200}{x} - \frac{200}{x + 5} = 2, x \in (- \infty, - 5) \cup (- 5, 0) \cup (0, + \infty)

Multiply both sides of the equation by LCD

(\frac{200}{x} - \frac{200}{x + 5}) x (x + 5) = 2 x (x + 5)

Simplify the equation

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1000 = 2 x (x + 5)

Simplify the equation

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1000 = 2 x^{2} + 10 x

Swap the sides of the equation

2 x^{2} + 10 x = 1000

Move the expression to the left side

2 x^{2} + 10 x - 1000 = 0

Factor the expression

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2 (x - 20) (x + 25) = 0

Divide the terms

(x - 20) (x + 25) = 0

When the product of factors equals 0,at least one factor is 0

x - 20 = 0 x + 25 = 0

Solve the equation for x

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x = 20 x + 25 = 0

Solve the equation for x

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x = 20 x = - 25

Check if the solution is in the defined range

x = 20 x = - 25, x \in (- \infty, - 5) \cup (- 5, 0) \cup (0, + \infty)

Find the intersection of the solution and the defined range

x = 20 x = - 25

Solution

x_{1} = - 25, x_{2} = 20

Show Solution