# How do you use the quotient rule to differentiate (4x − 2) / (x^2 + 1)?

Aug 4, 2016

$4 \cdot \frac{- {x}^{2} + x + 1}{{x}^{4} + 2 \cdot {x}^{2} + 1}$

#### Explanation:

The differential coefficient of a fraction is given by (Denominator * Diff. Coeff. of Numerator - Numerator * Diff. Coeff. of Denominator) / Denominator^2
Here DC of Denominator = 2x
and DC of Numerator = 4
Substituting we get
$\frac{\left({x}^{2} + 1\right) \cdot 4 - \left(4 x - 2\right) \cdot 2 x}{{x}^{2} + 1} ^ 2$
Expanding we get $\frac{4 \cdot {x}^{2} + 4 - 8 \cdot {x}^{2} + 4 \cdot x}{{x}^{4} + 2 \cdot {x}^{2} + 1}$
Simplifying, we get
$\frac{- 4 \cdot {x}^{2} + 4 \cdot x + 4}{{x}^{4} + 2 \cdot {x}^{2} + 1}$
ie $4 \cdot \frac{- {x}^{2} + x + 1}{{x}^{4} + 2 \cdot {x}^{2} + 1}$

Hope it is clear