Solve 1 over 2.7421 equals 1 over 3.3 plus 1 over x, for x.

Step-by-step solution

1. 1

   Isolate $\frac1x$.

   $\frac1x=\frac{1}{2.7421}-\frac{1}{3.3}$

   Here $2.7421<3.3$, so this difference is positive and $x$ will be positive — the combination sits below both parts, as a parallel/reciprocal combination should.

2. 2

   Combine the two fractions in one move. The identity $\frac1a-\frac1b=\frac{b-a}{ab}$ avoids computing two decimals separately and subtracting:

   $\frac1x=\frac{3.3-2.7421}{2.7421\times 3.3}$

3. 3

   Compute the numerator and the denominator carefully.

   $3.3-2.7421=0.5579,\qquad 2.7421\times 3.3=9.04893$

   That product is worth double-checking: $2.7421\times 3=8.2263$ and $2.7421\times 0.3=0.82263$, and $8.2263+0.82263=9.04893$. A frequently seen slip records it as $9.04993$, which shifts the final answer in the fourth significant figure.

4. 4

   Invert the quotient.

   $x=\frac{9.04893}{0.5579}=16.21963$

   Using the erroneous $9.04993$ instead would give $16.2214$ — close, but wrong past three decimals.

5. 5

   Verify by substitution. $\frac{1}{3.3}=0.3030303$ and $\frac{1}{16.21963}=0.0616537$; their sum is $0.3646840$, which equals $\frac{1}{2.7421}=0.3646840$ ✓. So $x\approx 16.2196$.