200/(15+x) + 200/(15-x) = 200

Let's solve the equation step by step:

Given: \[ \frac{200}{15 + x} + \frac{200}{15 - x} = 200 \]

Step 1: Find a common denominator

The denominators are \(15 + x\) and \(15 - x\). The common denominator is \((15 + x)(15 - x)\).

Step 2: Write the equation with a common denominator

\[ \frac{200(15 - x)}{(15 + x)(15 - x)} + \frac{200(15 + x)}{(15 + x)(15 - x)} = 200 \]

Combine the numerators:

\[ \frac{200(15 - x) + 200(15 + x)}{(15 + x)(15 - x)} = 200 \]

Step 3: Simplify numerator

\[ 200(15 - x) + 200(15 + x) = 200 \times 15 - 200x + 200 \times 15 + 200x \]

\[ = (200 \times 15 + 200 \times 15) + (-200x + 200x) = 2 \times 200 \times 15 + 0 = 2 \times 200 \times 15 \]

Calculate:

\[ 2 \times 200 \times 15 = 2 \times 200 \times 15 = 2 \times 3000 = 6000 \]

Step 4: Rewrite the equation

\[ \frac{6000}{(15 + x)(15 - x)} = 200 \]

Recall that:

\[ (15 + x)(15 - x) = 15^2 - x^2 = 225 - x^2 \]

So, the equation becomes:

\[ \frac{6000}{225 - x^2} = 200 \]

Step 5: Cross-multiplied

\[ 6000 = 200 (225 - x^2) \]

Divide both sides by 200:

\[ \frac{6000}{200} = 225 - x^2 \]

\[ 30 = 225 - x^2 \]

Step 6: Solve for \(x^2\)

\[ x^2 = 225 - 30 = 195 \]

Step 7: Find \(x\)

\[ x = \pm \sqrt{195} \]

Simplify \(\sqrt{195}\):

\[ 195 = 39 \times 5 \]

So:

\[ x = \pm \sqrt{39 \times 5} = \pm \sqrt{39} \times \sqrt{5} \]

If needed, approximate:

\[ \sqrt{39} \approx 6.245, \quad \sqrt{5} \approx 2.236 \] \[ x \approx \pm 6.245 \times 2.236 \approx \pm 13.96 \]

Final answer:

\[ \boxed{ x = \pm \sqrt{195} \approx \pm 13.96 } \]