How to solve (x(4)/(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 (x(4)/(x-1)) | Equatix

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Question

$$(x \frac{ 4 }{ x-1 } )$$

Differentiate w.r.t. x

$-\frac{4}{\left(x-1\right)^{2}}$

Steps Using Derivative Rule for Quotient

Express $x\times \frac{4}{x-1}$ as a single fraction.

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

For any two differentiable functions, the derivative of the quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared.

$$\frac{\left(x^{1}-1\right)\frac{\mathrm{d}}{\mathrm{d}x}(4x^{1})-4x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-1)}{\left(x^{1}-1\right)^{2}}$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is $0$. The derivative of $ax^{n}$ is $nax^{n-1}$.

$$\frac{\left(x^{1}-1\right)\times 4x^{1-1}-4x^{1}x^{1-1}}{\left(x^{1}-1\right)^{2}}$$

Do the arithmetic.

$$\frac{\left(x^{1}-1\right)\times 4x^{0}-4x^{1}x^{0}}{\left(x^{1}-1\right)^{2}}$$

Expand using distributive property.

$$\frac{x^{1}\times 4x^{0}-4x^{0}-4x^{1}x^{0}}{\left(x^{1}-1\right)^{2}}$$

To multiply powers of the same base, add their exponents.

$$\frac{4x^{1}-4x^{0}-4x^{1}}{\left(x^{1}-1\right)^{2}}$$

Combine like terms.

$$\frac{\left(4-4\right)x^{1}-4x^{0}}{\left(x^{1}-1\right)^{2}}$$

Subtract $4$ from $4$.

$$\frac{-4x^{0}}{\left(x^{1}-1\right)^{2}}$$

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

$$\frac{-4x^{0}}{\left(x-1\right)^{2}}$$

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

$$\frac{-4}{\left(x-1\right)^{2}}$$

Show Solution

Evaluate

$\frac{4x}{x-1}$

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Example

Question

Differentiate w.r.t. x

Steps Using Derivative Rule for Quotient

Evaluate

Solution Steps