How to solve (5a)/4 - (3a)/4

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 (5a)/4 - (3a)/4 | Equatix

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Question

$$\frac{5a}{4}-\frac{3a}{4}$$

Evaluate

$\frac{a}{2}$

Short Solution Steps

Since $\frac{5a}{4}$ and $\frac{3a}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{5a-3a}{4}$$

Combine like terms in $5a-3a$.

$$\frac{2a}{4}$$

Divide $2a$ by $4$ to get $\frac{1}{2}a$.

$$\frac{1}{2}a$$

Show Solution

Differentiate w.r.t. a

$\frac{1}{2} = 0.5$

Steps Using Definition of a Derivative

Since $\frac{5a}{4}$ and $\frac{3a}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5a-3a}{4})$$

Combine like terms in $5a-3a$.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2a}{4})$$

Divide $2a$ by $4$ to get $\frac{1}{2}a$.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{2}a)$$

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

$$\frac{1}{2}a^{1-1}$$

Subtract $1$ from $1$.

$$\frac{1}{2}a^{0}$$

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

$$\frac{1}{2}\times 1$$

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

$$\frac{1}{2}$$