Solve for x x+2=15/x

Problem

x+2=15/x

Solution

1. Multiply both sides of the equation by x to eliminate the fraction, assuming x≠0

x*(x+2)=15

2. Distribute the x on the left side.

x^2+2*x=15

3. Rearrange the equation into standard quadratic form a*x^2+b*x+c=0 by subtracting 15 from both sides.

x^2+2*x−15=0

4. Factor the quadratic expression by finding two numbers that multiply to −15 and add to 2

(x+5)*(x−3)=0

5. Apply the zero product property by setting each factor equal to zero.

x+5=0⇒x=−5

x−3=0⇒x=3

Final Answer

x=−5,3

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