Solve the equation
(x/x+2) - (4/x-2) = 1

Solve The Equation (x/x+2) - (4/x-2) = 1

Answers

Answer 1

Answer:

           [tex]\bold{x=-\dfrac23}[/tex]

Step-by-step explanation:

[tex]\dfrac x{x+2}-\dfrac4{x-2}=1\qquad\qquad\qquad x\ne2\ \wedge\ x\ne-2\\\\\\ \dfrac {x(x-2)}{(x+2)(x-2)}-\dfrac{4(x+2)}{(x-2)(x+2)}=1\\\\\\ \dfrac {x^2-2x-4x-8}{x^2-4}=1\\\\ \\\dfrac {x^2-6x-8}{x^2-4}=1\quad\iff\quad x^2-6x-8=x^2-4\\\\x^2-6x-8=x^2-4\\\\-6x-8=-4\\\\-6x=4\\\\x=-\frac46\\\\x=-\frac23[/tex]

Answer 2

The solution to the equation is x = -2/3.

What is an equation?

Two or more expressions with an equal sign are defined as an equation.

The given equation is  [tex]\frac{x}{x+2}-\frac{4}{x-2}=1[/tex].

Solve the equation as follows:
[tex]\frac{x}{x+2}-\frac{4}{x-2}=1\\\\\frac{x(x-2)-4(x+2)}{(x+2)(x-2)}=1\\\\\frac{x^2-2x-4x-8}{x^2-4}=1\\\\x^2-6x-8= x^2-4\\\\-6x = 8-4\\\\6x = -4\\\\x=-\frac{2}{3}[/tex]

Hence, the solution to the equation is x = -2/3.

Learn more about equations here:

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Answers

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Answers

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Answers

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Step-by-step explanation:

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