How to solve 6x/5-x/1

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 6x/5-x/1 | Equatix

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Question

$$6x/5-x/1$$

Evaluate

$\frac{x}{5}$

Short Solution Steps

Anything divided by one gives itself.

$$\frac{6x}{5}-x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $x$ times $\frac{5}{5}$.

$$\frac{6x}{5}-\frac{5x}{5}$$

Since $\frac{6x}{5}$ and $\frac{5x}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{6x-5x}{5}$$

Combine like terms in $6x-5x$.

$$\frac{x}{5}$$

Show Solution

Differentiate w.r.t. x

$\frac{1}{5} = 0.2$

Steps Using Definition of a Derivative

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x}{5}-x)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $x$ times $\frac{5}{5}$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x}{5}-\frac{5x}{5})$$

Since $\frac{6x}{5}$ and $\frac{5x}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x-5x}{5})$$

Combine like terms in $6x-5x$.

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

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

$$\frac{1}{5}x^{1-1}$$

Subtract $1$ from $1$.

$$\frac{1}{5}x^{0}$$

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

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

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

$$\frac{1}{5}$$