Solve (f+g)(x)=(2(x)^(2)+4x-6)+(2x-2) | 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

$$(f+g)(x)=(2 { x }^{ 2 } +4x-6)+(2x-2)$$

Solve for f

$f=2x-g+6-\frac{8}{x}$
$x\neq 0$

Steps for Solving Linear Equation

Use the distributive property to multiply $f+g$ by $x$.

$$fx+gx=2x^{2}+4x-6+2x-2$$

Combine $4x$ and $2x$ to get $6x$.

$$fx+gx=2x^{2}+6x-6-2$$

Subtract $2$ from $-6$ to get $-8$.

$$fx+gx=2x^{2}+6x-8$$

Subtract $gx$ from both sides.

$$fx=2x^{2}+6x-8-gx$$

The equation is in standard form.

$$xf=2x^{2}-gx+6x-8$$

Divide both sides by $x$.

$$\frac{xf}{x}=\frac{2x^{2}-gx+6x-8}{x}$$

Dividing by $x$ undoes the multiplication by $x$.

$$f=\frac{2x^{2}-gx+6x-8}{x}$$

Divide $2x^{2}+6x-8-gx$ by $x$.

$$f=2x-g+6-\frac{8}{x}$$

Solve for g

$g=2x-f+6-\frac{8}{x}$
$x\neq 0$

Steps for Solving Linear Equation

Use the distributive property to multiply $f+g$ by $x$.

$$fx+gx=2x^{2}+4x-6+2x-2$$

Combine $4x$ and $2x$ to get $6x$.

$$fx+gx=2x^{2}+6x-6-2$$

Subtract $2$ from $-6$ to get $-8$.

$$fx+gx=2x^{2}+6x-8$$

Subtract $fx$ from both sides.

$$gx=2x^{2}+6x-8-fx$$

The equation is in standard form.

$$xg=2x^{2}-fx+6x-8$$

Divide both sides by $x$.

$$\frac{xg}{x}=\frac{2x^{2}-fx+6x-8}{x}$$

Dividing by $x$ undoes the multiplication by $x$.

$$g=\frac{2x^{2}-fx+6x-8}{x}$$

Divide $2x^{2}+6x-8-fx$ by $x$.

$$g=2x-f+6-\frac{8}{x}$$