Solve 1/x − 1/( x + 1) = 4

Solve 1/x − 1/( x + 1) = 4 Give your answer in the form a ± b√2 where a and b are fractions.

To solve the equation 1/x – 1/(x + 1) = 4 and express the answer in surd form, we first need to find a common denominator for the fractions on the left side of the equation. Multiplying the first fraction by (x + 1)/(x + 1), we get (x + 1)/(x(x + 1)) – 1/(x + 1). This gives us (x + 1 – x)/(x(x + 1)) = 4. Simplifying further, we get 1/(x(x + 1)) = 4.

Next, we can cross multiply to solve for x in the denominator. This gives us x(x + 1) = 1/4. Multiplying out the left side, we get x^2 + x = 1/4. Rearranging the equation, we get x^2 + x – 1/4 = 0. This is a quadratic equation that can be solved using the quadratic formula.

Using the quadratic formula x = [-b ± √(b^2 – 4ac)] / 2a, where a = 1, b = 1, and c = -1/4, we can plug in these values to find the solutions for x in surd form. After solving for the discriminant and applying the formula, we get x = (-1 ± √(1 + 1))/2. Therefore, the solutions for x in surd form are x = (-1 ± √2)/2. This is the final answer for the equation given in surd form.

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