On rationalising the denominator, (√7 + √3)/(√7 − √3) becomes:

Multiply above and below by the conjugate √7 + √3. The numerator becomes $(\surd 7+\surd 3{)}^2=7+2$√21 + 3 = 10 + 2√21, and the denominator becomes 7 − 3 = 4. So the value is (10 + 2√21)/4 = (5 + √21)/2 ≈ 4.79, which matches 4.378 ÷ 0.914.