How to solve ((x)^(2))/(x)

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.

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Question

$$\frac{ { x }^{ 2 } }{ x }$$

Evaluate

$x$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{2}}{x^{1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$x^{2-1}$$

Subtract $1$ from $2$.

$$x^{1}$$

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

$$x$$

Show Solution

Differentiate w.r.t. x

$1$

Steps Using Derivative Rule for Product

Solution Steps

Steps Using Derivative Rule for Product

For any two differentiable functions, the derivative of the product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first.

$$x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x})+\frac{1}{x}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2})$$

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 $nax^{n-1}$.

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

Simplify.

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

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

$$-x^{2-2}+2x^{-1+1}$$

Simplify.

$$-x^{0}+2x^{0}$$

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

$$-1+2\times 1$$

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

$$-1+2$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})$$

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 $nax^{n-1}$.

$$x^{1-1}$$

Do the arithmetic.

$$x^{0}$$

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

$$1$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Evaluate

Steps Using Quotient of Powers Property

Differentiate w.r.t. x

Steps Using Derivative Rule for Product

Solution Steps

Steps Using Derivative Rule for Product

Solution Steps