Solve Addional i forall(x+ 1 2 )( matrix x-1\\ 2\\ 19a-b matrix )=x^ 2 - 1 x^ 6 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$( x + \frac { 1 } { 2 } ) ( x - \frac { 1 } { 2 } ) = x ^ { 2 } - \frac { 1 } { x }$$

Solve for x

$x=4$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $2x$, the least common multiple of $2,x$.

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

Use the distributive property to multiply $x+\frac{1}{2}$ by $x-\frac{1}{2}$ and combine like terms.

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

Use the distributive property to multiply $x^{2}-\frac{1}{4}$ by $2$.

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

Use the distributive property to multiply $2x^{2}-\frac{1}{2}$ by $x$.

$$2x^{3}-\frac{1}{2}x=2xx^{2}-2$$

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$2x^{3}-\frac{1}{2}x=2x^{3}-2$$

Subtract $2x^{3}$ from both sides.

$$2x^{3}-\frac{1}{2}x-2x^{3}=-2$$

Combine $2x^{3}$ and $-2x^{3}$ to get $0$.

$$-\frac{1}{2}x=-2$$

Multiply both sides by $-2$, the reciprocal of $-\frac{1}{2}$.

$$x=-2\left(-2\right)$$

Multiply $-2$ and $-2$ to get $4$.

$$x=4$$