How to solve x/5; 2/8

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve x/5; 2/8 | Equatix

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Question

$$\frac{x}{5}; \frac{2}{8}$$

Evaluate

$\frac{x}{20}$

Solution Steps

Reduce the fraction $\frac{2}{8}$ to lowest terms by extracting and canceling out $2$.

$$\frac{x}{5}\times \frac{1}{4}$$

Multiply $\frac{x}{5}$ times $\frac{1}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{x}{5\times 4}$$

Multiply $5$ and $4$ to get $20$.

$$\frac{x}{20}$$

Show Solution

Differentiate w.r.t. x

$\frac{1}{20} = 0.05$

Steps Using Definition of a Derivative

Reduce the fraction $\frac{2}{8}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{5}\times \frac{1}{4})$$

Multiply $\frac{x}{5}$ times $\frac{1}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{5\times 4})$$

Multiply $5$ and $4$ to get $20$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{20})$$

The derivative of $ax^{n}$ is $nax^{n-1}$.

$$\frac{1}{20}x^{1-1}$$

Subtract $1$ from $1$.

$$\frac{1}{20}x^{0}$$

For any term $t$ except $0$, $t^{0}=1$.

$$\frac{1}{20}\times 1$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$\frac{1}{20}$$